{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[](https://colab.research.google.com/github/PerformanceEstimation/PEPit/blob/master/ressources/demo/PEPit_demo_extract_worst_case_examples.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PEPit : numerical identification of worst-case examples"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook provides:\n",
"- A simple example illustrating how to obtain a worst-case instance for **gradient descent** (when minimizing a smooth convex function) using the PEPit package.\n",
"- Four other examples illustrating how to obtain worst-case instances in other situations: with proximal operators, momentum, possibly non-convex functions, and primal-dual methods.\n",
"\n",
"For a first demo of PEPit, including detailed installation, imports, and basic introductory steps, we refer to the introductory [demo](https://colab.research.google.com/github/bgoujaud/PEPit/blob/master/ressources/demo/PEPit_demo.ipynb) file.\n",
"\n",
"\n",
"This notebook considers the following four algorithms:\n",
"* [Example 1](#example1) : **gradient descent** for smooth convex minimization (1D examples).\n",
"* [Example 2](#example2) : the **fast iterative shrinkage-thresholding algorithm** (FISTA) for composite convex minimization (1D examples).\n",
"* [Example 3](#example3) : **gradient descent** for smooth possibly non-convex minimization (1D examples).\n",
"* [Example 4](#example4) : an **alternating projection algorithm** for finding a point in intersection of two convex sets (2D examples).\n",
"* [Example 5](#example5) : a primal-dual **proximal-point algorithm** for convex (possibly non-smooth) minimization (2D examples).\n",
"* [Example 6](#example6) : **gradient descent with exact line-search** for smooth strongly convex minimization (2D examples)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Import a few necessary common Python packages (numpy, matplotlib)**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib\n",
"matplotlib.rcParams.update({\n",
" \"mathtext.fontset\": \"cm\", # LaTeX font for rendering equations in plots\n",
" \"legend.fontsize\": 12,\n",
" \"axes.labelsize\": 14\n",
"})\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from math import sqrt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Table of Contents\n",
"- [1. Gradient descent for smooth convex minimization](#example1)\n",
"- [2. FISTA for composite convex minimization](#example2)\n",
"- [3. Gradient descent for smooth possibly non-convex minimization](#example3)\n",
"- [4. Alternate projections](#example4)\n",
"- [5. Primal-dual proximal-point](#example5)\n",
"- [6. Gradient descent with exact line-search](#example6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We re-implement some basic examples below. This is necessary as we will save the worst-case trajectories."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1 : gradient descent for smooth convex minimization \n",
"\n",
"We consider the following convex minimization problem:\n",
"\\begin{equation}\n",
"f_\\star \\triangleq \\min_x f(x),\n",
"\\end{equation}\n",
"where $f$ is $L$-smooth and convex.\n",
"\n",
"For this example, we consider the problem of computing the smallest possible $\\tau(n, L, \\gamma)$ such that the following guarantee holds (for any initialization of the algorithm, and any $L$-smooth convex functions)\n",
"\\begin{equation}\n",
"f(x_n)-f_\\star \\leqslant \\tau(n, L, \\gamma) \\| x_0 - x_\\star \\|^2,\n",
"\\end{equation}\n",
"where $x_n$ is the output of gradient descent with fixed step size $\\gamma$, started from $x_0$, and where $x_\\star$ is a minimizer of $f$.\n",
"\n",
"#### Algorithm\n",
"\n",
"Gradient descent with fixed step size $\\gamma$ may be described as follows, for $t \\in \\{0,1, \\ldots, n-1\\}$\n",
"\\begin{equation}\n",
"x_{t+1} = x_t - \\gamma \\nabla f(x_t).\n",
"\\end{equation}\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Low-dimensional worst-case examples\n",
"\n",
"The solution to the PEP provides an example trajectory of points that would result in a worst-case convergence rate. In general, worst-case examples are non-unique in different ways: there are generally many trajectories of points that result in worst-case performance, and there are generally multiple different functions that can interpolate the same trajectory. Using a solution to the PEP, one can identify the dimension of a matching worst-case instance by inspection of the rank of the Gram matrix. More precisely, the rank of the Gram matrix corresponds to the dimension of the matching worst-case example (see, e.g., [here, Section 3.2](https://arxiv.org/pdf/1502.05666)).\n",
"\n",
"PEPit contains a few heuristics to try to identify such low-dimensional worst-case instances, by searching for low-rank Gram matrices. There are two of them: the trace heuristic ($\\ell_1$ on the eigenvalues) and the logdet heuristic---applying gradient descent on the logdet of the Gram matrix $G$, which corresponds to a reweighted $\\ell_1$ on the eigenvalues of $G$. For both of them, we need to potentially leave some slack in the objective, which we fix here to `tol_dimension_reduction=1e-6`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 1 function(s)\n",
"\t\t\tFunction 1 : Adding 30 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 30 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 0 function(s)\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 7x7\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.05555555533811466\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 4.671407470112186e-08 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.055554555299553596\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 1.7470776746371454e-09 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -4.18e-11 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 4.1801938146378587e-11\n",
"\t\tAll the primal scalar constraints are verified up to an error of 7.835664582456214e-11\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative up to an error of 2.8401468021662646e-09\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 4.100136013346356e-08\n",
"(PEPit) Final upper bound (dual): 0.05555555838910858 and lower bound (primal example): 0.055554555299553596 \n",
"(PEPit) Duality gap: absolute: 1.0030895549809071e-06 and relative: 1.805593707972616e-05\n"
]
}
],
"source": [
"from PEPit import PEP\n",
"from PEPit.functions import SmoothStronglyConvexFunction\n",
"\n",
"L = 1\n",
"gamma = 1/L\n",
"n = 4\n",
"verbose = 1\n",
"\n",
"\n",
"# Instantiate PEP\n",
"problem = PEP()\n",
"\n",
"# Declare a smooth strongly convex function\n",
"f = problem.declare_function(SmoothStronglyConvexFunction, L=L,mu=0)\n",
"\n",
"# Then define the starting point x0 of the algorithm as well as corresponding gradient and function value g0 and f0\n",
"x0 = problem.set_initial_point()\n",
"g0, f0 = f.oracle(x0)\n",
"\n",
"xs = f.stationary_point()\n",
"gs, fs = f.oracle(xs)\n",
"\n",
"# Prepare empty lists for saving all datapoints\n",
"x_list = list()\n",
"g_list = list()\n",
"f_list = list()\n",
"\n",
"# Run n steps of GD method with step-size gamma\n",
"gx, fx = g0, f0\n",
"\n",
"x_list.append(x0)\n",
"g_list.append(g0)\n",
"f_list.append(f0)\n",
"\n",
"for i in range(n):\n",
" x_list.append(x_list[-1] - gamma * gx)\n",
" gx, fx = f.oracle(x_list[-1])\n",
" g_list.append(gx)\n",
" f_list.append(fx)\n",
" \n",
"# Set initial condition and performance metric\n",
"problem.set_initial_condition((x0-xs)**2 <= 1)\n",
"problem.set_performance_metric(f_list[-1] - fs)\n",
"\n",
"# Solve the PEP\n",
"pepit_verbose = max(verbose, 0)\n",
"pepit_tau = problem.solve(verbose=pepit_verbose, dimension_reduction_heuristic=\"trace\", tol_dimension_reduction=1e-6)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see from the output, PEPit identified a low-rank matrix where all eigenvalues (except one) is approximately equal to 0. This corresponds to a single-dimensional worst-case example.\n",
"In order to evaluate and plot a worst-case trajectory, we use the `eval` function on the iterates, their gradients, and function values. Since we want to visualize the worst-case in 1D, we trim the dimension to only the first components."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Evaluate the iterations:\n",
"\n",
"x_list_evaluated = [x.eval()[0] for x in x_list] # [0] is because we are interested in largest component only\n",
"g_list_evaluated = [g.eval()[0] for g in g_list] # same\n",
"f_list_evaluated = [f.eval() for f in f_list]\n",
"\n",
"# Evaluate specific points (for better visualization later)\n",
"xs_evaluated = xs.eval()[0] # x*\n",
"gs_evaluated = gs.eval()[0] # g(x*)=0\n",
"fs_evaluated = fs.eval() # f(x*)\n",
"\n",
"x0_evaluated = x0.eval()[0] # x0\n",
"g0_evaluated = g0.eval()[0] # g(x0)\n",
"f0_evaluated = f0.eval() # f(x0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, using the list of iterates, we can simply plot the trajectory (in terms of $(x,f(x))$ as follows: "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x_list_evaluated, f_list_evaluated, '.--', color='blue')\n",
"\n",
"plt.plot(x_list_evaluated, f_list_evaluated, marker='.', color='red', linestyle='none', markersize=8, label='$(x_t,f(x_t))$')\n",
"plt.plot(xs_evaluated, fs_evaluated, marker='*', color='gold', linestyle='none', markersize=10, label=r'$(x_\\star,f(x_\\star))$')\n",
"plt.plot(x0_evaluated, f0_evaluated, marker='s', color='green', linestyle='none', markersize=5, label=r'$(x_0,f(x_0))$')\n",
"\n",
"\n",
"plt.legend()\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$f(x)$')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The last plot is giving a partial picture of what a worst-case function might look like: the function is evaluated only at a few points (iterates & an optimal point).\n",
"\n",
"For this reason, we provide a few tools that allows extrapolating within certain classes of functions. This is done via the \"interpolator\" classes (that internally formulate the interpolation problems for a few classes).\n",
"\n",
"The interpolator that corresponds to the PEP under consideration can be obtained (when implemented for the corresponding class) as follows (possibly with a few options):"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"feval = f.get_interpolator()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we can evaluate an interpolating function on a grid of points \"x_test\" around the iterates and the solution."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100 / 100 grid points computed\r"
]
}
],
"source": [
"# Create a grid of points where an interpolating function should be computed:\n",
"nb_pts_grid = 100\n",
"x_min = np.min([x0_evaluated,xs_evaluated])\n",
"x_max = np.max([x0_evaluated,xs_evaluated])\n",
"x_test = np.linspace(x_min,x_max,nb_pts_grid)\n",
"\n",
"# Use the interpolation tools: evaluate a function using the \"feval\" interpolator on the grid:\n",
"fx_test = np.zeros(x_test.shape)\n",
"for i in range(len(x_test)):\n",
" fx_test[i] = feval(np.array([x_test[i]]))\n",
" print(f'{i + 1} / {len(x_test)} grid points computed', end='\\r', flush=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"... which we can now plot!"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plt.plot(x_list_evaluated[::1,], f_list_evaluated, '.--', color='blue')\n",
"plt.plot(x_test, fx_test, '--', color='blue', label='$(x,f(x))$')\n",
"plt.plot(x_list_evaluated, f_list_evaluated, marker='.', color='red', linestyle='none', markersize=8, label='$(x_t,f(x_t))$')\n",
"plt.plot(xs_evaluated, fs_evaluated, marker='*', color='gold', linestyle='none', markersize=8, label=r'$(x_\\star,f(x_\\star))$')\n",
"\n",
"\n",
"plt.legend()\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$f(x)$')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We observe a trajectory that looks like a type of Huber loss function, as predicted by the proof of Theorem 3.2 from [this paper](https://arxiv.org/pdf/1206.3209)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2 : FISTA for composite convex minimization \n",
"\n",
"We consider the following convex minimization problem:\n",
"\\begin{equation}\n",
"F_\\star \\triangleq \\min_x f(x)+h(x),\n",
"\\end{equation}\n",
"where $f$ is $L$-smooth and convex, and where $h$ is convex (closed, proper) with a proximal operator readily available.\n",
"\n",
"For this example, we consider the problem of computing the smallest possible $\\tau(n, L)$ such that the following guarantee holds (for any initialization of the algorithm, and any $L$-smooth convex function)\n",
"\\begin{equation}\n",
"F(x_n)-F_\\star \\leqslant \\tau(n, L) \\| x_0 - x_\\star \\|^2,\n",
"\\end{equation}\n",
"where $x_n$ is the output of the FISTA initiated at $x_0$, and where $x_\\star$ is a minimizer of $F$.\n",
"\n",
"#### Algorithm\n",
"\n",
"The iterates of FISTA are described as (for $t \\in \\{0,1, \\ldots, n-1\\}$)\n",
"$$\n",
"\\begin{aligned}\n",
" \\lambda_{t+1} & = &\\frac{1 + \\sqrt{4\\lambda_t^2 + 1}}{2}\\\\\n",
" x_t & = &\\mathrm{argmin}_x \\left\\{h(x)+\\frac{L}{2}\\left\\|x-\\left(y_t - \\frac{1}{L} \\nabla f(y_t)\\right)\\right\\|^2 \\right\\}\\\\\n",
" y_{t+1} & = & x_t + \\frac{\\lambda_t-1}{\\lambda_{t+1}} (x_t-x_{t-1}).\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"Let us first start by importing all the necessary packages for the implementation in PEPit (this is done [there](https://pepit.readthedocs.io/en/0.4.0/examples/b.html#accelerated-proximal-gradient-a-k-a-fista), which we use below)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"from math import sqrt\n",
"from PEPit import PEP\n",
"from PEPit.functions import SmoothConvexFunction\n",
"from PEPit.functions import ConvexFunction\n",
"from PEPit.primitive_steps import proximal_step"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following lines adapt the previous code to the study of FISTA:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 2 function(s)\n",
"\t\t\tFunction 1 : Adding 20 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 20 scalar constraint(s) added\n",
"\t\t\tFunction 2 : Adding 12 scalar constraint(s) ...\n",
"\t\t\tFunction 2 : 12 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 0 function(s)\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 10x10\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.0761787865456547\n",
"(PEPit) Postprocessing: 3 eigenvalue(s) > 7.47573367793566e-08 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.07617778646356368\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 3.6860755232230394e-09 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -9.4e-11 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 9.395236189612535e-11\n",
"\t\tAll the primal scalar constraints are verified up to an error of 1.9884285537563606e-10\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 5.799556179640622e-08\n",
"(PEPit) Final upper bound (dual): 0.0761787908371793 and lower bound (primal example): 0.07617778646356368 \n",
"(PEPit) Duality gap: absolute: 1.0043736156095662e-06 and relative: 1.3184599635091319e-05\n"
]
}
],
"source": [
"# Parameters / options for the study:\n",
"verbose = 1 # verbose\n",
"n = 3 # number of iterations\n",
"L = 1 # Lipschitz constant\n",
"\n",
"# Performance estimation problem (PEP) formulation:\n",
"\n",
"# Instantiate PEP\n",
"problem = PEP()\n",
"\n",
"# Declare a strongly convex smooth function and a convex function\n",
"f = problem.declare_function(SmoothConvexFunction, L=L)\n",
"h = problem.declare_function(ConvexFunction)\n",
"F = f + h\n",
"\n",
"# Start by defining an optimal point xs = x_* and its function value Fs = F(x_*)\n",
"xs = F.stationary_point()\n",
"Fs = F(xs)\n",
"gs, fs = f.oracle(xs) # this is g(xs)=f'(x_*)\n",
"ss, hs = -gs, Fs - fs # this is s(xs) \\in \\partial h(x_*) and hs = Fs - fs\n",
"\n",
"# Create empty lists for saving a worst-case trajectory\n",
"y_list = list() # list of points where we will evaluate f() and its gradient\n",
"g_list = list() # list of evaluated gradients of f() at y's\n",
"f_list = list() # list of evaluated f() at y's\n",
"x_list = list() # list of outputs of the proximal operator\n",
"s_list = list() # list of evaluated subgradients of h() at x's (outputs of prox)\n",
"h_list = list() # list of evaluated h() at x's (outputs of prox)\n",
"\n",
"# Then define a starting point x0\n",
"x0 = problem.set_initial_point()\n",
"g0, f0 = f.oracle(x0)\n",
"# Set the initial constraint that is the distance between x0 and x^*\n",
"problem.set_initial_condition((x0 - xs) ** 2 <= 1)\n",
"\n",
"# Compute n steps of FISTA starting from x0 \t\n",
"x_new = x0\n",
"y = x0\n",
"lam = 1\n",
"for i in range(n):\n",
" # update momentum parameters\n",
" lam_old = lam\n",
" lam = (1 + sqrt(4 * lam_old ** 2 + 1)) / 2\n",
" \n",
" # save old point for momentum\n",
" x_old = x_new\n",
" \n",
" # evaluate gradient at y + save corresponding values\n",
" gy, fy = f.oracle(y)\n",
" y_list.append(y)\n",
" g_list.append(gy)\n",
" f_list.append(fy)\n",
" \n",
" # perform a proximal-gradient step\n",
" x_new, sx_new, hx_new = proximal_step(y - 1 / L * gy, h, 1 / L)\n",
" \n",
" # save outputs/subgradient of h() at x (output of prox)\n",
" x_list.append(x_new)\n",
" s_list.append(sx_new)\n",
" h_list.append(hx_new)\n",
" \n",
" y = x_new + (lam_old - 1) / lam * (x_new - x_old)\n",
"\n",
"# Since we evaluate the performance of the algorithm at x_n, we add it to the y_list (list of points at which f() is evaluated)\n",
"gx, fx = f.oracle(x_new)\n",
"y_list.append(x_new)\n",
"g_list.append(gx)\n",
"f_list.append(fx) \n",
"\n",
"# Set the performance metric to the function value accuracy\n",
"problem.set_performance_metric((fx + hx_new) - Fs)\n",
"\n",
"# Solve the PEP\n",
"pepit_verbose = max(verbose, 0)\n",
"pepit_tau = problem.solve(verbose=pepit_verbose, dimension_reduction_heuristic=\"trace\", tol_dimension_reduction=1e-6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us clean and evaluate the different lists, in order to plot the corresponding functions:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Evaluation of the trajectories:\n",
"y_list_evaluated = [y.eval()[0] for y in y_list] # centered iterates (evaluations of f() )\n",
"x_list_evaluated = [x.eval()[0] for x in x_list] # centered iterates (evaluations of h() )\n",
"\n",
"g_list_evaluated = [g.eval()[0] for g in g_list] # gradient values for f\n",
"s_list_evaluated = [s.eval()[0] for s in s_list] # gradient values for h\n",
"\n",
"f_list_evaluated = [f.eval() for f in f_list] # centered function values\n",
"h_list_evaluated = [h.eval() for h in h_list] # centered function values\n",
"\n",
"# Evaluations at the optimal point:\n",
"xs_evaluated = xs.eval()[0] # x*\n",
"gs_evaluated = gs.eval()[0] # g(x*)=0\n",
"fs_evaluated = fs.eval() # f(x*)\n",
"ss_evaluated = -gs_evaluated # s(x*) \\in\\partial h(x*)\n",
"hs_evaluated = Fs.eval()\n",
"\n",
"# Evaluations at x0\n",
"x0_evaluated = x0.eval()[0] # x*\n",
"g0_evaluated = g0.eval()[0] # g(x*)=0\n",
"f0_evaluated = f0.eval() # f(x*)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now plot the iterates on the two functions (in terms of $(y,f(y))$ and $(x,f(x))$, side to side:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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kiICq43//+58efPBBJSQkKDg42OxwnFrdunU1a9Ys/e9//1OXLl2UmJioFi1amB2Wy+LcqzicmygN8ioAuIh8pOzIPyoPd0o5mbwrrlS+Co9inyeLzgZdZVJEQNUxd+5cDRo0iItwKURERKhp06ZatWqV2aG4NM69ise5CXsUl1ed9ievAlD9kI+UH/lHxaMo5WQ8n59su7VcsiZO7jI0+uhkLVlicnCAi/v999/l6+tbYp9169Zp/fr1Doro8pwhnlq1aikzM9PUGFydK557f+WM8XFu4nKKy6v+fnyyoqOlnByTAwQAB3L1fMRZYiP/qFgUpZzNgAHSsmXKa9dBeZ7eyrmygyZds1wfZ/fXoEHS009LFy6YHSRQNf34449atWqVevbsaXYokiounqeffrrIC2dx7XA8Zzv3/qqy4ivpHOT8RIX4S16V17aDPh60XCvUX3PmSL17SykpZgcJAM7B0fnIhAkTdMstt2jUqFGX7VuRsZEbOxeKUs5owAB57t0p9+xzqnlgpyZt768nnrAuevll6YMPzA0PqKomTJigiRMnmrLvuLg4jRkzRrfddpvS0tIqNJ7o6GiNHTvW7nY4npnn3l9V5rn4VyWdg5yfqDB/yqs8v9+pIYv7a+VKycdH2rBBiooyO0AAcA6OzkemTZsmLy8v1apV67J9KzI2cmPnQlHKBXh4SK+8Ii1eLEVGSg8+aHZEQNWTmJiohg0bXvaW5soQHx+vefPmqX///tq2bZsyMzMrNJ6goCC1adNGn376qV3tcCwzz72/quxz8a9KOgc5P1GZ7rhD2rpV6tlTmj3b7GgAwHxm5CPu7u7at2+funXrVmK/io6N3Ni5UJRyIYMGSZ9+Krm7W99nZ0uMrwaUjsViKbL9zTff1P333+/gaKyWLVumnj17qlevXkpNTVWzZs0qPJ7Ro0drxowZdrf/mZeXl7KzsyssFldy/PhxvfzyyyX2efnll+2aGtgZz72/csS5+FclnYOXOz+r87mJ8rvySmndOqlVq4ttq1dL58+bFxMAVDZnykdSUlL0yy+/KCwsrMR+lREbubHzoCjlwh57TLrzTmnMGAbqhBNavlzq2FGqWdP6c/lyU8O5cOGCfvzxR7Vp06bI5Rs2bFBISIiDo7JKTEy85GJc0fH4+fnJ19dXu3btsqv9z+6++24tW7ZMZ8+erbB4XEVOTs5lj/vs2bPKKeGPsDOfe3/liHPxr0o6By93flbncxMV77PPrHlVz57S4cNmRwPA5ZELX9bGjRsVGBioli1bltivMmIjN3YeHmYHgLIxDCkw0Pr77NnSzp3SkiUX2wBTLV8uDRwoWSzWk3X3buv7Zcusg846WGZmph5++GFFRERoyJAhlyz/8ccf5e/vL09Pz0uWLViwQLt27VJubq5ef/11SVJGRoauvfZa7dixQz4+PmWO66OPPtKqVau0e/durVq1St98841mzZqlU6dOFRlPeWPp3r271qxZow4dOtjVXmDUqFGqV6+ehg8frmHDhql///5lPubqpjznXm5urqZPny6LxaLk5GS98MILmj9/vjIzM9W5c2cNGzaswuIs7blY0bGVdA6WtIxzExXJ21uqV0/atk0KCZE++US6+WazowLgkqpQLlyZ+UhiYqKuu+46vfzyyzIMQ3v27NGwYcPUp0+fy8ZWEXGRGzsH7pRyURaLNGWKCg3Ued11UlKS2ZEBkqZOvXgRlqw/LRbpueccHkpGRoY6d+6sm266Se+//77c3C79s3fs2DE1atTokvb9+/erRo0aGjBggN577z1be2Jion7//XfVqVOnXLHdd999io2NlYeHhxYvXqwPP/xQ9erVKzKeioilY8eO2rlzp93tf+bm5iYPDw/l5ubadWwo37knSXPmzNE999yjp556Si1atFBERIRiY2O1ZcsW/fe//63QWEtzLlZGbCWdg5c7Pzk3y27OnDlq2bKlvL29FRoaqi1btpTYf8mSJQoODpa3t7euueYaff7554WWT5kyRcHBwapdu7bq1aun8PBwbd68uTIPoUL17i0lJ0vXXiudOiXdcos0ffrFSxkA2K2K5MJS5eYjGzdu1MGDBzVixAg9/fTTGjRokMaPH29XbBURF7mxc+BOKRdXMFBn//7S999LN94ozZol/f3v1r97gCl++OHSLN4wpAMHHB6Kj4+PNm3apIceekhJSUl6++23L7kYnzx5ssiBE9etW6f7779fM2bMUOfOnW3tSUlJ6tmzZ5EX9dL67rvvFBwcLC8vrxLjqYhY6tevr59//tnu9gLvv/++pk+frvXr16tevXr2HFapfPDBBzIMQ5mZmWratKkGDhxY4fswQ3nOPUny8PBQ69atJUmnTp3SHXfcoVq1aunNN99UkyZNKjxee8/FyoitpHOwpGWVfW5WZYsXL1ZMTIzmzp2r0NBQzZw5UxERETpw4ECRyX9iYqKGDh2quLg43X777Vq0aJEiIyO1fft2tW/fXpJ05ZVXavbs2WrdurXOnTunGTNm6NZbb9VPP/2khg0bOvoQy6RlS2njRmse9eGH0rhx1jzr3Xel2rXNjg6Ay6giubBUefnI+fPntWPHDn366ae2684ff/xxyZhXlZmLOGtuXOCzzz7TmTNnnGbs0crCnVJVwJVXSps3S3ffLeXmSrGx0okTZkeFau3KKy+tilos0lVXmRKOn5+fPv74Y61Zs0aLFy++ZHl+fn6R640ePVo1a9bUihUrNGjQIFt7UlKSbrzxRtv7m266qcyxfffdd+rUqdNl46mIWOrVq6f09HS72wt88sknGjRoULEX3fIc//Hjx/Xvf/9bDz74oB599FG98MILVWrgyLKee5J1WuICiYmJ6tGjhyTrt3eV8T/49p6LlRFbSedgScsud26ieNOnT9eoUaM0cuRItWvXTnPnzlWtWrX0/vvvF9n/9ddfV58+ffTkk0+qbdu2mjZtmq677jrN/tPUdffee6/Cw8PVunVrXX311Zo+fboyMjJKHJfDGdWsKc2fL73xhnUG5I8/to43BQB2qyK5sGT/Nb+0+eDWrVvl7u6u8PBwW9v69esvGTuqInKR4mJzxtxYkgzD0Jtvvqnp06crLy+vXNtyBRSlqog6daxjH7z0krRwoRQQYHZEqNYmT754m7J08fblyZNNC8nDw0Nt2rTRDz/8cMkyf39/paWlFbnemTNnlJycrNtuu02S9SKxZcsWWyFo//798vf3L3Ncu3btUseOHe2Kp7yx5OXlFTlWQHHtBc6fP1/s8vIe/7p163TdddfZ3gcFBSnJiZ5Ddnd3v2wykJeXJw+P4m88Luu5V+DEiRM6cOCALdmqLKU5Fys6tpLOwZKWlXRuong5OTlKTk4u9D8Cbm5uCg8PL/a/v6SkpEL9JSkiIqLY/jk5OXr77bfl6+t7yXlVIDs7WxkZGYVezsJikaKjpa+/liZMsM6ADAB2q0K5cIGSrvllyQcTExPVpUsX23XcMAytXLlSffv2LVVsl8tFSorNGXNjyTpD4j//+U/17NmzXNtxFTy+V4VYLNJTTxVuS0iQ3NwYqBMONmCAdSDH556z3qZ81VXWi7ATDAJoFDE4SOPGjXX69Oki+//888/y9fVVixYtJEnff/+9DMNQp06dtHbtWr311ltq2LChli9frgFlGLhy586dlzw7X1w85Y3l999/L/IuluLaL6cijv/YsWOFBmivW7eujh8/XurtlEZycrK+/fZbZWVlqW3btkpPT9fZs2c1ZsyYS/o2btxYe/fulWEYRU6hbBiG9u3bp0A7ZpkozbmXm5ur9evXq1evXlq/fr1atmxp28fatWvVokULnT171u7jsIe956I9sbVt27ZUn3NJ52BZz08U79SpU8rLy1PAX77BCggI0P79+4tcJyUlpcj+KSkphdpWr16tIUOG6OzZs2rcuLHi4+OLTc7j4uI0derUchxJ5evRw/oqcOqU9NFH0qOPWvMrAChSFcmF7bnm//rrr2XKBzdu3FiokLRhwwalpaWpT58+mj9/vu6++27Vrl27XLnI5XJVZ8yNzVCanK0ycDmtwn791frNHgN1whQDBlinhTx3zvrTCS7CxQkODlZqaqouXLhwybK6desqNzfXdrfMv//9b11//fVyd3dXnz59ZLFYNH78+EIXnXnz5ikoKEinTp0qcb+HDx/W6dOnL7mLoLh4yhLLn506darIZ+yLa7+c4vb566+/aubMmcW+/vwNXX5+fqG7jC5cuCB3d/dSx1Iap06dUnBwsH744QfdfffdioyM1DfffFNkXw8PD919990aMWKEUlNTCy1LTU3VyJEjdffdd5d4p1RJivu3fvfdd9W3b1+dPXtWa9assSVGOTk5SkhIUNu2be06jso4F+2JTSrd51zSOVjW8xPmuPnmm7Vz504lJiaqT58+GjRokE4UM6ZAbGys0tPTba8jR444ONrSyc+Xhg6Vxo61XuJKeLIDAKpELmzPNb+s+fCfH7mTpC1btigsLEw1a9ZUSkqKav//QH7lyUUulx87KjeWSpcfO1ppcrbKwJ1SVVijRtJttzFQJ3A5bm5uCg0N1XfffXfJc+zBwcF69NFHFRMTo0aNGumzzz7TP/7xD0nWgsovv/yiK664otA6+fn5On/+vDZt2qTbb7+92P0WDBD8129iiounLLH82bZt2woNkn659sspbp8tWrTQ448/btc2mjZtqqNHj9reZ2RkqHHjxqWOpTQiIiIUExOje++9V5L05Zdflvj42b333qt27dpp4sSJyszMtLXXqVNHjz/++CXjMJVGcf/WPXr00F133aW4uDhFR0fr7bff1sSJE2UYhsaNG2f3cVTGuWhPbPbGV6Ckc7Cs5yeK5+/vL3d39yILrcXd9RcYGGhX/9q1a+uKK67QFVdcoW7duqlNmzZ67733FBsbe8k2vby8Cg2s7+zc3KxFqXXrpP/+VwoNlT79VPr///cBAJdVnnykLPlwWlqa6tSpUygv6Nevnz7//HPFxsZq7NixJcZmby5yufzYUbmxVLr82NFKmxtXOANllp6ebkgy0tPTzQ6lWPn5hjFrlmF4eBiGZBgdOhjGTz+ZHRWcyblz54zvv//eOHfunNmhVLobb7zRmDx5cpHL1qxZY8TGxhZqy87ONh555BHjwIEDhmEYxm+//WbUqVPHOHLkiGEYhrF9+3bjvvvuM/Ly8ozPP/+80LppaWnGsmXLitzXs88+ayQmJhrPPPOM8fTTT9sVT3liKdC7d2/jhx9+sLu9QJcuXYyZM2de0l7cPg8ePGi88sorxb72799v65uSkmLceOONhmEYRl5entGmTRsjMzPTMAzD+OWXX4y8vLxL9rt582bj2LFjtvdfffWVkZaWZnv/2WefGTk5OSVuIyQkxLafyMhI47fffjO++OKLYj+D8irtuWcve46jos/Fio7PMEo+B0taVty5WRR7/ta5wnW9onTt2tWIjo62vc/LyzOaNm1qxMXFFdl/0KBBxu23316oLSwszPj73/9e4n5at25d7Ln/V67y+W/ZYhjNmlnzqjp1DGP5crMjAlAe5MJWZb3elzUfLo3KiM0wHJcbG0bp8uMCkydPNj744APbe2fLjS/3346913WKUuXgKsmTYRjGunWGERBgTaD8/AxjzRqzI4KzqE4X4ttvv92IiYkpdnm/fv2MrKws2/vNmzcbderUMXbs2GFbf/bs2bblv/76q/HQQw8ZCxYssP0RL7By5Urj0KFDl+zjxIkThoeHh7F69WrjxhtvNH4qoUr853jKE4thGMaRI0eMm2++2e72AmvWrDGaNGlS5LFcbp/2mj59uvHvf//beP755wslLh06dDD+97//XdL/oYceMj766CPb+4iICOPbb7+1vb/66qttn2tR2/jjjz+M2267zfb+kUceMebPn2/89ttvZT6GyyntuWcPe4+jos/Fio6vpHOwpGUlnZtFoShV2Mcff2x4eXkZ8+bNM77//ntj9OjRhp+fn5GSkmIYhmHcf//9xvjx4239N27caHh4eBivvvqqsW/fPmPy5MlGjRo1jN27dxuGYRiZmZlGbGyskZSUZBw6dMjYtm2bMXLkSMPLy8vYs2ePXTG50uefmmoYN91kzaskw5gwwTAuXDA7KgBlQS58UVmu92XJh8uiomNz5tzYMAzjnXfeMbp3727069fPWLx4sWEYzpcbU5RyAq6UPBmGYRw9ahjdulmTp6gos6OBs6hOF+K1a9cazZo1M7Zv317k8s2bNxe6WyQ7O9t49tlnjbi4OGPs2LF2f9OTk5NjTJs2rchl+fn5xujRo43x48cbb7/9donb+XM8ZY2lwFNPPWV89dVXdrenp6cbY8aMMcaOHWucPHmyVPuqKNnZ2caaclbQK2IbFaG0515FqYxzsaIVdw4Wt6ys5yZFqUu98cYbRvPmzQ1PT0+ja9euxqZNm2zLbrzxRuOBBx4o1P+TTz4xrrzySsPT09O4+uqrjc8++8y27Ny5c0b//v2NJk2aGJ6enkbjxo2NO++809iyZYvd8bja55+baxhjx1rzqr/9zTD+9KU0ABdCLnxRRV7vS8pByqKicxFy4/KrqKKUxTAY/rqsMjIy5Ovrq/T09EKzRzmz7Gxpxgzp8cclb2+zo4EzOH/+vA4ePKhWrVrJuxqcFPv27dMrr7yipk2batq0aZcs/+STT9SgQQP17t27zPs4dOiQataseclMVWVREfHs3LlT8+bN08yZM+1qdxarVq1S7969VatWLVO3UVEcce79lbOdi39V0jlY0eenPX/rXPG6XpW46uf/n/9IV18tdehgdiQAyoJcuLCKut5XZA5SoKJiIzeumNz4cv/t2HtdpyhVDq6aPP1ZXp702GPSI48wUGd1Vd0uxNXRCy+8oKeeeko1atSwq91ZZGZmqk6dOqZvA5WnpHOwos9PilLOr6p8/u++K9WqJf3/eLEAnBy5cPVDblwxuTFFKSdQFZKnl16Sxo+X6tSRFixw6plKUUm4EAOoDihKOb+q8Pnv3i2FhEi5udYv/V55RXLS/7cB8P/IhYGyqaiilFtlBgnnN3KkdOONUmamNGCA9Mwz1runAAAAUDrt2klPPWX9/fXXpVtukVJTzY0JAABnRlGqmmvUSIqPl8aOtb5/8UXpttukM2fMjQsAAMDVuLtLzz8vLV8u1a0rffut9c6pLVvMjgwAAOdEUQqqUUOaPl1auFCqWVP63/+kzp2lXbvMjgwAAMD19O9vLUQFB0vHjkk9e0rvvWd2VAAAOB+KUrC5914pKUlq1Ur67Tce4wMAACir4GBp82ZrgSonRzp50uyIAABwPh5mBwDn0rGjtG2blJwsXXut2dEAAAC4Lh8faelS6+N8AweaHQ0AAM6HO6Vwifr1rQNzFtiyRYqIYKBOAACA0nJzk+6+W7JYrO8zM6151rp15sYFAIAzoCiFEuXnW2fo++ILBuoEAAAorxdflL78UurdW5o1SzIMsyMCAMA8FKVQIjc3adky6aqrGKgTAACgvCZOtI7jeeGC9Nhj0vDh0tmzZkcFAIA5KErhsoKDrXdIRUZaB+p86CHpH/+QsrPNjgwAAMC11KolffSRNGOG5O5u/f3666VDh8yODAAAx6MoBbv4+FjvmHr+eeuYCP/+t3TTTVJamtmRAQAAuBaLRXr8cetjfA0bSjt3WodJSEw0OzIAAByLohTs5uYmPfOM9Nlnkp+f1KiRtVgFAACA0rvpJuuMx126SDVqSC1amB0RAACO5WF2AHA9fftaE6gGDayFKknKzZU8PC7OLAM4o3Xr1slisahnz55mh2IXV4sXAFB6QUHWmfh++UVq2vRie26utVAFABXFVXNLV40b9uFOKZRJ69aSr6/1d8OQHnxQeuABBuqE8/rxxx+1atUql7mYOTrep59+WpmZmXa3AwAqjre31K7dxfdLl0rXXiv98IN5MQGoWpwpF54wYYJuueUWjRo16rJ9HRl3SXkvOXHloSiFcvvuO+k//5E+/JCBOvEX2Xuko5HWnyabMGGCJk6caHYYRYqLi9OYMWN02223Ke3/B2pzdLzR0dEaO3as3e0AgMpx4YJ1uIS9e62P9a1caXZEAMqMXLhI06ZNk5eXl2rVqnXZvo6Mu6S8l5y48lCUQrl16iTFxxceqDM+3uyo4BQyV0uZ/5UyPzM1jMTERDVs2FC+Bbf3OZH4+HjNmzdP/fv317Zt25SZmWlKvEFBQWrTpo0+/fRTu9oBAJXDw0P69lupRw8pI0O66y5p8mQpP9/syACUGrlwkdzd3bVv3z5169atxH6OjrukvJecuPJQlEKFuPnmiwN1njkj9ekjvfSS9dE+VGNZXxX+aZI333xT999/v6kxFGfZsmXq2bOnevXqpdTUVDVr1sy0eEePHq0ZM2bY3Q4AqByBgVJCgjRmjPX9c89Jd9wh/f67uXEBKCVy4SKlpKTol19+UVhYWIn9zIi7pLyXnLhyUJRChSkYqDMqyvpt3vjx0sMPmx0VHCr3qHR++/+/kqVz663t59ZZ3xcsyz3m0LA2bNigkJAQh+7TXomJiZdckM2K18/PT76+vtq1a5dd7QCAyuPpKc2aJS1YYB1z6vPPrV/+ZWSYHRmAYpEL22Xjxo0KDAxUy5YtS+xnRtwl5b3kxJWD2fdQoby9pXfesSZNY8dKgwebHREc6uhtUvaf/0j//3SMRrZ0qPPFZq8OUqvvHBLSjz/+KH9/f3l6ehZqz83N1fTp02WxWJScnKwXXnhB8+fPV2Zmpjp37qxhw4ZValwfffSRVq1apd27d2vVqlX65ptvNGvWLJ06darIeB0Vc/fu3bVmzRp16NDBrnYAQOW6/37p6qulAQOsj/L5+JgdEYBikQvbJTExUdddd51efvllGYahPXv2aNiwYerTp49TxF1S3ktOXPFc6k6pOXPmqGXLlvL29lZoaKi2bNlSYv8lS5YoODhY3t7euuaaa/T5558XWj5ixAhZLJZCrz//h4CysVikv//dOuD5zTdfbD950rSQ4Ch17/5Lg/GXnwX97nFENJKkY8eOqVGjRpe0z5kzR/fcc4+eeuoptWjRQhEREYqNjdWWLVv03//+t9Ljuu+++xQbGysPDw8tXrxYH374oerVq1dsvI6KuWPHjtq5c6fd7QCAynfdddL27dahEQr8/rt1UHQAToRc2C4bN27UwYMHNWLECD399NMaNGiQxo8f7zRxl5T3khNXPJe5U2rx4sWKiYnR3LlzFRoaqpkzZyoiIkIHDhwo8mRNTEzU0KFDFRcXp9tvv12LFi1SZGSktm/frvbt29v69enTRx988IHtvZeXl0OOpzr48z/LgQNSaKj02GPWwTrdXKocCrv5P2v9eWpSCX2mSf6Om/nj5MmTRQ6O6OHhodatW0uSTp06pTvuuEO1atXSm2++qSZNmpS4TcMwZLFYyh3bd999p+Dg4EJ/d4qL11Ex169fXz///LPd7QAAx6hf/+LvOTnWMaa8vKSPP7ZONgPACZALX9b58+e1Y8cOffrpp7b/j//jjz8u2Z6ZcZeU95ITVzyXKQ1Mnz5do0aN0siRI9WuXTvNnTtXtWrV0vvvv19k/9dff119+vTRk08+qbZt22ratGm67rrrNHv27EL9vLy8FBgYaHvVq1fPEYdT7fz3v1J6+sWBOv9/1ntURf7PSvViil5Wf5xDL8KSlF/MdEXR0dG23xMTE9WjRw9J1m8/GpaQ3f/+++8V9hz5d999p06dOhVqKy5eyTEx16tXT+np6Xa3AwAcb88e64zHX30lde5snWwGgJMgFy7R1q1b5e7urvDwcFvb+vXrLxk7ysy4S8p7yYkrnksUpXJycpScnFzoxHVzc1N4eLiSkpKKXCcpKalQf0mKiIi4pP8333yjRo0a6aqrrtLDDz+s06dPV/wBQE89delAnXv2mB0VKs8FWZ+hL/gm4v9/Nxz/nIG/v7/SSqiCnjhxQgcOHLBd0C5n+/bt2rZtW4XEtmvXLnXs2LFQ2+XilSo35ry8vCLHsyquHQDgeNddJ23eLLVpIx0+LF1/vTRvntlRAbiIXLg4iYmJ6tKliy2vNAxDK1euVN++fZ0m7pLyXnLiiucSRalTp04pLy9PAQEBhdoDAgKUkpJS5DopKSmX7d+nTx8tWLBACQkJeumll/Ttt9+qb9++ysvLK3Kb2dnZysjIKPSC/e6/X9q4UWrRQvrpJ6lbN+mTT8yOChXOyJcyPpZkSG6+UoNJ1p8ypIz/WJc7UOPGjS8pNufm5uqrr6xT865fv14tW7ZUYGCgJGnt2rXat29fof6pqalat26dDh06pC1btmjLli06evSoEhMTdfDgwTLHtnPnzkvulCoqXkfG/Pvvvxf5LVNx7QAAc1x9tbRli3T77VJ2tjRypBQdbX20D4CJyIVLtHHjxkKFpA0bNigtLU19+vTR/PnzlZWVZXrcJeW95MQVzyWKUpVlyJAhuvPOO3XNNdcoMjJSq1ev1tatW/XNN98U2T8uLk6+vr62V1BQkGMDrgKuu07atk0KD5eysqyz8zlgTGk4knFO8giS6vSXWh+QGk61/qzTX6rR3LrcgYKDg5WamqoLfxoN9t1331Xfvn119uxZrVmzxnZhycnJUUJCgtq2bVtoGwEBAfr99991ww03aMKECXr77bfVoUMH7dmzp8ipbOfNm6egoCCdOnWq2LgOHz6s06dPX3KnVFHxOiLmAqdOnSryefzi2gEA5vHzs+ZRU6ZY38+ZI/3jH2ZGBIBcuORc+M+P3EnSli1bFBYWppo1ayolJUW1a9c2Le4CJeW95MQVzyWKUv7+/nJ3d1dqamqh9tTUVFtl9K8CAwNL1V+SWrduLX9/f/30009FLo+NjVV6errtdeTIkVIeCSTJ319as8b6SF/PnlK/fmZHhArlVltquVlqtlzy+P/R7j0aWd+32GRd7shw3NwUGhqq7767OO1ujx49dNdddykuLk7R0dHq3LmzJk6cqKlTp2rcuHFFbueuu+6yfTMjSf/5z380evToIgdLzM/P1/nz57Vp06Zi4yqYdOGv37QUFa8jYi6wbds2de7c2e52AIC53Nysk8isWiU1by49/bTZEQHVHLlwsblwWlqa6tSpU6go1a9fPxmGodjYWD3wwAOmxl2gpLyXnLjiWQzDMC7fzXyhoaHq2rWr3njjDUnWE7158+aKjo6+ZPpISRo8eLDOnj2rVatW2dq6d++uDh06aO7cuUXu4+jRo2revLlWrFihO++887IxZWRkyNfXV+np6fLx8SnjkVVvOTlSwSO5Fy5YZ+m7+mpzY6puzp8/r4MHD6pVq1by9vY2O5xKsXbtWq1bt04vvvhiubYzdepU/fHHH2revLmSk5M1f/78Yvump6crISFBAwYMKNQ+adIk9e3bV5999pkuXLigf/3rX5UWb2ljlqTw8HC99dZbatOmjV3tgKuw528d13Vz8fmX35/zKkn67jupQwepAiaMBaoscmH7VUQuXBpmxC2VnPeSE190uf927L2uu8SdUpIUExOjd955R/Pnz9e+ffv08MMPKysrSyNHjpQkDR8+XLGxsbb+jz32mNauXavXXntN+/fv15QpU7Rt2zbbaP2ZmZl68skntWnTJh06dEgJCQm66667dMUVVygiIsKUY6yO/pw4PfWUFBIiXeZvBFBqffr00XfffaezZ8+WeRu5ublq2rSpXn31VT366KPq27evzpw5U2z/devWXTKLyMmTJxUXF6czZ85ow4YNGjVqVKXFW5aYjx49qvz8/EsussW1AwCcy5/zqq++sg6b8OCD0vnz5sUEwHzOkguXlhlxl5T3khNXDpcpSg0ePFivvvqqJk2apE6dOmnnzp1au3atbTDzw4cP67fffrP17969uxYtWqS3335bHTt21NKlS7VixQq1b99ekuTu7q5du3bpzjvv1JVXXqmoqCiFhIRo/fr18vLyMuUYq7MLF6Qff7QO1DliBAN1ouJNnjxZzz33XJnX9/Dw0EMPPWR7P2TIENWrV6/Ivrm5ufruu+/UokWLQu3+/v568MEHtWHDBg0bNkx/+9vfKi3e0sYsSW+88YaeffZZu9sBAM5r/37rz3nzpB49rLP0Aai+nCEXLgtHxi2VnPeSE1cOl3l8zxlxm3nFys+Xpk27OFjn9ddLS5ZIjRubGlaVVx1uWS7wySefqEGDBurdu3el7ufQoUOqWbPmJTOAlpaj4pWsMwHOmzdPM2fOtKsdcDU8vuf8+Pwr3pdfSkOGSKdPW8f0XLxY6tXL7KgA50IuXPEqKhcu4Ki4S8p7yYkvVVGP73lUZpBAaRQM1BkSIt13n7Rxo/X3pUul7t3Njg5VwaBBgxyyn5Jm8ygNR8UrSZ999pleeeUVu9sBAM4vPFxKTpYGDJC2b5duuUV66SVp3DjGmQKqI1fLhQs4Ku6S8l5y4srjMo/vofq4/XZp61brgOe//SbdcYd0buFy5bTrqDzPmspp11FavtzsMIEq5ZlnnlGNGjXsbgcAuIYWLaQNG6QHHrDelf7kk9ZZkAEAhZWU95ITVx7ulIJTatNG2rRJioqSHm++XDXvG6h8WeQmQ5Z9u6WBA6Vly6xf/QEAAKBYNWtKH3wgde1qvWOqb1+zIwIAwIo7peC06tSxjn0Q8tlUW0FKktxkKE8W5TxbvkGgAQCozubMmaOWLVvK29tboaGh2rJlS4n9lyxZouDgYHl7e+uaa67R559/bluWm5urp59+Wtdcc41q166tJk2aaPjw4Tp+/HhlHwbsZLFI//yn9O67Fx/dS0+X4uPNjQsAUL1RlILTc//pB1tBytYmQ+4/HTApIgAAXNvixYsVExOjyZMna/v27erYsaMiIiJ04sSJIvsnJiZq6NChioqK0o4dOxQZGanIyEjt2bNHknT27Flt375dzz77rLZv367ly5frwIEDuvPOOx15WCiF/Hzp/vuliAjrRDP5+WZHBACojihKwenlXXGl8lV4NM48WXSi3lVi7kgAAEpv+vTpGjVqlEaOHKl27dpp7ty5qlWrlt5///0i+7/++uvq06ePnnzySbVt21bTpk3Tddddp9mzZ0uSfH19FR8fr0GDBumqq65St27dNHv2bCUnJ+vw4cOOPDTYKS9PatZMMgxp0iSpf3/rnVMAADgSRSk4Pc/nJ9se2ZOsBSl3Gfpn6mTde6+UlWVygFWEQYUPQBXG37iLcnJylJycrPDwcFubm5ubwsPDlZSUVOQ6SUlJhfpLUkRERLH9JSk9PV0Wi0V+fn5FLs/OzlZGRkahFxynRg3pzTel99+XvLyklSutY059/73ZkQHm4DoBlE5F/TdDUQrOb8AAadky5bXroDxPb+W17aDPH1qu1R799fHHUliY9PPPZgfpujw8rPMdXLhwweRIAKDyFPyNK/ibV52dOnVKeXl5CggIKNQeEBCglJSUItdJSUkpVf/z58/r6aef1tChQ+Xj41Nkn7i4OPn6+tpeQUFBZTgalNfIkdL69VJQkPTDD1JoKJMco3ohFwbKJjc3V5Lk7u5eru1QlIJrGDBAnnt3yj37nDy/36l+7/TXV19JAQHS7t3SSy+ZHaDrcnd3l7u7O99QA6jSMjIybH/vULlyc3M1aNAgGYaht956q9h+sbGxSk9Pt72OHDniwCjxZ126SNu2STfdJGVmSo8/Lp07Z3ZUgGOQCwOlZxiG0tPT5eXlpRo1apRrW3xdCJfVs6d1WuNnn5VmzDA7GtdlsVjUqFEj/fbbb/Ly8lLt2rVlsVguvyIAuADDMJSVlaWMjAw1btyYv2+S/P395e7urtTU1ELtqampCgwMLHKdwMBAu/oXFKR+/fVXffXVV8XeJSVJXl5e8vLyKuNRoKI1amSdiW/CBOmee6SaNc2OCHAMcmHAfoZhKDc3V+np6crMzFTTpk3LvU2KUnBpTZpI77138b1hSK+9Jo0aJfn6mheXq/H19dW5c+d06tQpnTx50uxwAKBCFYxr5MuFQZLk6empkJAQJSQkKDIyUpKUn5+vhIQERUdHF7lOWFiYEhIS9Pjjj9va4uPjFRYWZntfUJD68ccf9fXXX6tBgwaVeRioBB4e0ssvF25bulT629+ka681JybAEciFgdLx8vJS06ZNS/zyyV4UpVClvPyyNH689M470ooVUtu2ZkfkGiwWixo3bqxGjRrZng0GgKqiRo0aPLb3FzExMXrggQfUuXNnde3aVTNnzlRWVpZGjhwpSRo+fLiaNm2quLg4SdJjjz2mG2+8Ua+99ppuu+02ffzxx9q2bZvefvttSdaC1N13363t27dr9erVysvLs403Vb9+fXl6eppzoCiXHTuk+++3/r529HKFxU+V+08/KO+KK+X5/GTruJ9AFUAuDNjP3d293I/s/RlFKVQpvXpZpzf+4QfrDDLz55MvlQbjrQBA9TB48GCdPHlSkyZNUkpKijp16qS1a9faBjM/fPiw3NwuDj3avXt3LVq0SBMnTtSECRPUpk0brVixQu3bt5ckHTt2TCtXrpQkderUqdC+vv76a910000OOS5UrJYtpZtvlrzXLNeNswYqXxa5yZBl325p4EBp2TISLVQp5MKA41kM5r4ss4yMDPn6+io9Pb1CbltDxThxQho8WPrmG+v72Fhp2jSJ6wsAoCRc183F5++c8vKklICOanx6t9x08X8b8mRRXrsO8ty707zgAABOy97rOrPvocopGKgzJsb6Pi5O6tdPOn3a3LgAAABcjbu7FJjxQ6GClCS5y5D7TwdMigoAUFVQlEKV5OFhHfB80SLr7DFffy399JPZUQEAALievCuuVL4Kz0aWJ4vyrrjKpIgAAFUFRSlUaUOHSps2WceWCg01OxoAAADX4/n8ZLnJUN7/F6byZJG7DOtg5wAAlANFKVR5HTpYi1MFdu2SnnhCYmINAAAAOwwYIC1bprx2HZTn6a28dh2k5cul/v11/rw0erR09KjZQQIAXBFFKVQr2dnWvOq116TwcCk11eyIAAAAXMCAAfLcu1Pu2eesg5v37y9Jeuop6Z13pJAQ6dtvzQ0RAOB6KEqhWvHykl59VapbV1q3zppAbd5sdlQAAACuaexYqWNH6+zHvXtLr78uMbc3AMBeFKVQ7URGSlu2SMHB0rFj0g03SG+/bXZUAAAArqdVKykxURo2TMrLkx5/XLrvPunsWbMjAwC4AopSqJaCg62FqQEDpJwc6e9/l0aNsv4OAAAA+9WqJX34oTRzpuTubp39uHt36eBBsyMDADg7ilKoturWlZYulV58UbJYpMOHrYkUAAAASsdikR57TEpIkBo1sg58brGYHRUAwNl5mB0AYCaLRYqNlbp0ka69lqIUAABAedx4o5ScbP2yr2VLs6MBADg77pQCZJ2Jr0GDi+8feYSBOgEAAMqiWTPr43sFVq+W7r5b+uMP82ICADgn7pQC/uKrr6Q337T+vnWrdRD0WrXMjQkAAMAVnT0rRUVZZ+fbu1dasUK66iqzowIAOAvulAL+4uabLw7UuXChdP31DNQJAABQFrVqSStXSk2bSvv3W4dM+O9/zY4KAOAsKEoBf/HXgTp37pRCQqQvvjA7MgAAANcTGmodZ+qGG6yP8EVGSs8+K+XlmR0ZAMBsFKWAYhQM1Nm1q/T771KfPtZxpgAAAFA6AQHSl19av/iTpOefl+64Q8rJMTcuAIC5KEoBJWjWTFq3TnroIev7K680Nx4AAABXVaOGdYiEDz+UataUWrSQPD3NjgoAYCYGOgcuw8tLeucd6Z//lK699mJ7bq41uQIAAID97rvPmlNdccXFNvIqAKieuFMKsNOfC1IHD1rvmlq50rx4AAAAXNXVV1u/+JOkCxekfv2kJ56w/g4AqD4oSgFl8PLL0qFD0l13SZMmMVAnAABAWX35pfX12mvSrbdKJ0+aHREAwFEoSgFlMGuW9Oij1t+nTbMO1Pn77+bGBAAA4Ir69JGWLpXq1JG+/to66/HWrWZHBQBwBIpSQBnUqGGdie/DDyVvb2nNGqlLF2n3brMjAwAAcD0DB0qbN1uHRzhyROrZU3r/fbOjAgBUNopSQDncd5+UmCi1bCn9/LPUrZu0aZPZUQEAALiedu2kLVukO++UsrOlqCjrHekAgKqLohRQTtdeK23bJt1yi3XQzk6dzI4IAADANfn6Sp9+Kj33nFS3rtS/v9kRAQAqE0UpoAI0aGB9hG/NGuvjfJJ18PMzZ8yNCwAAwNW4uUnPPiv99JPUvv3FdgZAB4Cqh6IUUEHc3a3FqQKTJ1vvmtq2zbSQAAAAXFajRhd/LxguYc4cyTBMCwkAUMEoSgGV4OxZ6ywyR45IPXpIH3xgdkQAAACu6+OPrflVdLQ0cqR07pzZEQEAKgJFKaAS1KplnUGmYKDOBx+U/vlPKSfH7MgAAABcz+uvS6++an20b/5865d+v/5qdlQAgPKiKAVUkj8P1GmxSG+9Jd18s3T8uNmRAQAAuBaLRRo3ToqPl/z9pe3bpZAQKSHB7MgAAOVBUQqoRAUDda5ebS1SJSZKPXtyxxQAAEBZ9OolJSdbC1KnT0u33mq9Ox0A4Jo8zA4AqA769bMOeN6/v/TUU5Knp9kRAQAAuKbmzaX1661DI/zxh9S1q9kRAQDKiqIU4CBXXGH9Zu/PBakffpCCgqSaNc2LCwAAwNXUrCm9/76Um2t9tE+SMjOl1FTpb38zNzYAgP14fA9woD8XpE6ckHr3ZqBOAACAsrBYLuZWhiFFRVkf61u92ty4AAD2oygFmOTQIen8eQbqBAAAKK/MTOnoUSk9XbrjDmnqVCk/3+yoAACXQ1EKMEnXrtZxpv48UOcrr1i/6QMAAID96taVvv7aOs6UJE2ZIkVGWotUAADnRVEKMFGLFtaBOkeMsH6b99RT0pAh1m/7AACoTHPmzFHLli3l7e2t0NBQbdmypcT+S5YsUXBwsLy9vXXNNdfo888/L7R8+fLluvXWW9WgQQNZLBbt3LmzEqMHLuXpKc2ZI33wgeTlJa1aJXXpIu3da3ZkAIDiUJQCTFYwUOecOZKHh/TJJ9KkSWZHBQCoyhYvXqyYmBhNnjxZ27dvV8eOHRUREaETJ04U2T8xMVFDhw5VVFSUduzYocjISEVGRmrPnj22PllZWerRo4deeuklRx0GUKQRI6QNG6yTyfz4o/WOqQsXzI4KAFAUi2HwsFBZZWRkyNfXV+np6fLx8TE7HFQBGzdKEydK//2vxCkFAI5Vna7roaGh6tKli2bPni1Jys/PV1BQkMaMGaPx48df0n/w4MHKysrS6j+NIN2tWzd16tRJc+fOLdT30KFDatWqlXbs2KFOnTrZHVN1+vzhGCdPSsOHS888Y51YBgDgOPZe17lTCnAi119vHQ+h4L9Zw5CWL2egTgBAxcnJyVFycrLCw8NtbW5ubgoPD1dSUlKR6yQlJRXqL0kRERHF9rdHdna2MjIyCr2AitSwobRmTeGC1NdfW8fyBAA4B4pSgBObNUsaOFDq35+BOgEAFePUqVPKy8tTQEBAofaAgAClpKQUuU5KSkqp+tsjLi5Ovr6+tldQUFCZtwXYY88e68x8ISHSjh1mRwMAkFysKFXRA3L+2T/+8Q9ZLBbNnDmzgqMGys7PzzpQ58qV1tn6vv/e7IgAAKgYsbGxSk9Pt72OHDlidkio4iwWKTBQ+vVXqXt36cMPzY4IAOAyRanKGJCzwKeffqpNmzapSZMmlX0YQKk88MDFgTp/+MFamFq61OyoAACuzN/fX+7u7kpNTS3UnpqaqsDAwCLXCQwMLFV/e3h5ecnHx6fQC6hMV18tbdsm9esnnT9vHW/q0Uel3FyzIwOA6stlilLTp0/XqFGjNHLkSLVr105z585VrVq19P777xfZ//XXX1efPn305JNPqm3btpo2bZquu+4624CeBY4dO6YxY8Zo4cKFqlGjhiMOBSiVzp2l5GSpVy8pK0u65x5p/HgpL8/syAAArsjT01MhISFKSEiwteXn5yshIUFhYWFFrhMWFlaovyTFx8cX2x9wVn5+0qpVF2c6fuMNqXdvqRxPogIAysElilKVNSBnfn6+7r//fj355JO6+uqrLxsHA3LCLA0bSv/7n/TEE9b3r74q7dxpakgAABcWExOjd955R/Pnz9e+ffv08MMPKysrSyNHjpQkDR8+XLGxsbb+jz32mNauXavXXntN+/fv15QpU7Rt2zZFR0fb+pw5c0Y7d+7U9///rPmBAwe0c+fOco07BVQGNzdp6tSLsx2vXy/9+99mRwUA1ZOH2QHYo6QBOffv31/kOvYMyPnSSy/Jw8NDjz76qF1xxMXFaerUqaWMHqgYHh7SK69Y75w6edI6SCcAAGUxePBgnTx5UpMmTVJKSoo6deqktWvX2nKnw4cPy83t4neX3bt316JFizRx4kRNmDBBbdq00YoVK9S+fXtbn5UrV9qKWpI0ZMgQSdLkyZM1ZcoUxxwYUAp33ilt2SJNny4984zZ0QBA9eQSRanKkJycrNdff13bt2+XxWKxa53Y2FjFxMTY3mdkZDBTDBxu8ODC7/fvt46PcN995sQDAHBN0dHRhe50+rNvvvnmkrZ77rlH99xzT7HbGzFihEaMGFFB0QGOcdVVhe+SysmRZs60jjXl7W1aWABQbbjE43uVMSDn+vXrdeLECTVv3lweHh7y8PDQr7/+qnHjxqlly5ZFbpMBOeFsMjOl/v2l++9noE4AAIDyeuIJ6emnpRtukJgQEgAqn0sUpSpjQM77779fu3bt0s6dO22vJk2a6Mknn9T//ve/yjsYoALVqmUd+FxioE4AAIDyuv12qX59aetW61AJRdw0CACoQC5RlJIqfkDOBg0aqH379oVeNWrUUGBgoK666ipTjhEoLTc36bnnpBUrpLp1rQN1hoRImzaZHRkAAIDrufVW67AInTpZx/AMD5dmzJAMw+zIAKBqcpmi1ODBg/Xqq69q0qRJ6tSpk3bu3HnJgJy//fabrX/BgJxvv/22OnbsqKVLl14yICdQVdx1l/UbvbZtpePHrbecv/222VEBAAC4nlatpI0breN15uVJMTHW38+eNTsyAKh6LIZB3b+sMjIy5Ovrq/T0dMaXglP44w9p5Ehp2TJrYeqrryR3d7OjAgDXwHXdXHz+cDaGIc2ebS1K1aolJSdLV1xhdlQA4Brsva5X29n3gKqobl1pyRJp1ixpyBAKUgAAAGVlsUhjxkgdO0pZWRSkAKAyuMzjewDsY7FIjz0m/f+TrZKs4059+615MQEAALiqG26Q+va9+D4hQXrxRcaZAoCKQFEKqOJWrpQmT7bOzDdzJgkUAABAWZ0+LQ0eLD3zjDRwoJSRYXZEAODaKEoBVVx4+MWBOseOZaBOAACAsmrQQPrXvyRPT+nTT6XQUGn/frOjAgDXRVEKqOJq1ZIWLJBef906xtSiRVL37tIvv5gdGQAAgOt56CFp3TqpaVNrQaprV2nFCrOjAgDXRFEKqAYsFunRR62z8TVqJH33ndS5s/S//5kdGQAAgOsJDbXOxnfDDdbZj/v3lyZOlPLzzY4MAFwLRSmgGrnhBmsCFRoq/f67lJlpdkQAAACuKSBA+vJL6fHHre8PH7Z+EQgAsJ+H2QEAcKxmzawz8a1ZI0VGmh0NAACA66pRQ5oxQ7r5ZumWWyhKAUBpcacUUA15eRUuSB09Kj179XJl/q2j8jxrKqddR2n5ctPiAwAAcCV33inVrGn9PT9fGjLEOo4nAKBkFKUAaNHdyzXt+4Gq9ctuueeel8e+3dZ5jilMAQAAlMrChdLixdKwYdaZj3NzzY4IAJwXRSkAGnNmqvJlkZsMSZKbDOXJopxnnzM5MgAAANdy771SbKz195kzrY/1nThhakgA4LQoSgGQ56EfbAWpAu4y5P7jAZMiAgAAcE3u7tKLL0rLlkl16ljH8gwJkbZsMTsyAHA+FKUAKO+KK5WvwiNz5smi/bpKP/9sUlAAAAAubMAAayHqqqus43f27Cl9/LHZUQGAc6EoBUCez0+2PbInWQtS7jL0bpPJCgw0OTgAAAAX1battTB1113WmfmuuMLsiADAuVCUAmD9Km/ZMuW166A8T2/lteugP+Yv1+Pf9lft2tYu+fnShQvmhgkAAOBqfHysc8ds2iR17nyxnQHQAYCiFIACAwbIc+9OuWefk+fenao7vL9atLi4+F//km69VTp50rwQAQAAXJGbm9Sp08X3ycnSlVdK69ebFhIAOAWKUgAu6/Rp6eWXpa+/tg7UuXWr2REBAAC4rilTpEOHpF69pDfekAzjcmsAQNVEUQrAZTVoICUmWr/RO3LEOlDn+++bHRUAAIBr+vhjacgQ69AIjz4qPfCAdO6c2VEBgONRlAJgl3btrAN13nmnlJ0tRUVJDz8s5eSYHRkAAIBrqV1bWrRImj5dcneXPvxQuv56691TAFCdUJQCYDdfX+nTT6Vp06wzyMydax1nKj/f7MgAAABci8UijR0rxcdLDRtKO3ZYh0n48UezIwMAx6EoBaBU3NykiROl1aslPz9p6FBrGwAAAErv5putA5937iyFhUl/+5vZEQGA43iYHQAA19Svn3TggPWbvQInT0r+/tZv/gAAAGCfoCDrTHw5ORe/7Dt3zjrmVN265sYGAJWJ+xsAlFmjRhcLUGfOSKGhDNQJAABQFt7eko+P9XfDsI7d2a2b9MMP5sYFAJWJohSACvHtt9LhwwzUCQAAUF6pqdaxpr7/XurSRVq1yuyIAKByUJQCUCH697cmT/7+1oE6O3eWvvzS7KgAAABcT2CgdZypHj2kjAzr7MeTJzO5DICqh6IUgArz54E6T5+WIiKkV16x3oIOAAAA+wUGSgkJUnS09f1zz1mLU2lppoYFABWKohSACtW8uXWgzpEjrd/mPfWU9PLLZkcFAADgejw9pTfekObNs4459dlnUt++fOEHoOqgKAWgwnl7S++9J735pnTlldJDD5kdEQAAgOt64AFp40apdWtp2jRmOgZQdVCUAlApLBbrrDG7d0sNGlxs37XLvJgAABfNmTNHLVu2lLe3t0JDQ7Vly5YS+y9ZskTBwcHy9vbWNddco88//7zQcsMwNGnSJDVu3Fg1a9ZUeHi4fvzxx8o8BKBaue46ad8+KTz8YtvevdKFC+bFBADlRVEKQKXy9Lz4+zvvSB07SlOmMFAnAJhp8eLFiomJ0eTJk7V9+3Z17NhREREROnHiRJH9ExMTNXToUEVFRWnHjh2KjIxUZGSk9uzZY+vz8ssva9asWZo7d642b96s2rVrKyIiQufPn3fUYQFV3p/zqh9/tM543KePdOqUeTEBQHlQlALgMPv3W39OnSrddRcDdQKAWaZPn65Ro0Zp5MiRateunebOnatatWrp/fffL7L/66+/rj59+ujJJ59U27ZtNW3aNF133XWaPXu2JOtdUjNnztTEiRN11113qUOHDlqwYIGOHz+uFStWOPDIgOrjxx+td0klJFgnmfnl1eXKaddReZ41ldOuo7R8udkhAsBlUZQC4DCvvXZxoM7Vq6WuXaU/fckOAHCAnJwcJScnK/xPzwC5ubkpPDxcSUlJRa6TlJRUqL8kRURE2PofPHhQKSkphfr4+voqNDS02G0CKJ9+/aRNm6QrrpCu+3W5Wj85UB77dss997w89u2WBg6kMAXA6VGUAuBQBQN1Nm9u/YavWzfpk0/MjgoAqo9Tp04pLy9PAQEBhdoDAgKUkpJS5DopKSkl9i/4WZptZmdnKyMjo9ALQOm0by9t3Sq9Umeq8mWRm6zT8rnJUJ4synn2OZMjBICSUZQC4HDXXSclJ0u9e0tZWdLQodIPP5gdFQDAkeLi4uTr62t7BQUFmR0S4JL8/KSW2T/YClIF3GXI/acD5gQFAHaiKAXAFP7+0tq10lNPSc89J115pdkRAUD14O/vL3d3d6WmphZqT01NVWBgYJHrBAYGlti/4GdpthkbG6v09HTb68iRI2U6HgBS3hVXKl+Wwm2yKO+Kq0yKCADsQ1EKgGk8PKSXXpKeeeZi2y+/SNu3mxcTAFR1np6eCgkJUUJCgq0tPz9fCQkJCgsLK3KdsLCwQv0lKT4+3ta/VatWCgwMLNQnIyNDmzdvLnabXl5e8vHxKfQCUDaez0+2PbInWQtS7jLk+fxkkyMDgJJRlALgNM6elfr3t05vvGCB2dEAQNUVExOjd955R/Pnz9e+ffv08MMPKysrSyNHjpQkDR8+XLGxsbb+jz32mNauXavXXntN+/fv15QpU7Rt2zZFR0dLkiwWix5//HE9//zzWrlypXbv3q3hw4erSZMmioyMNOMQgeplwABp2TLlteugPE9v5bXrYB3kvH9/syMDgBJ5mB0AABTIzbUOgL5rl3VA9C1bpOnTJU9PsyMDgKpl8ODBOnnypCZNmqSUlBR16tRJa9eutQ1UfvjwYbm5Xfzusnv37lq0aJEmTpyoCRMmqE2bNlqxYoXat29v6/PUU08pKytLo0ePVlpamnr06KG1a9fK29vb4ccHVEsDBshzwABJkrvJoQCAvSyGYRiX74aiZGRkyNfXV+np6dxyDlSQ/HzrGFNTp1rf9+ghLVkiFTMkCQBUGK7r5uLzBwCg6rD3us7jewCcipubNGWKtHKl5OMjbdhgna0vKcnsyAAAAAAAFYmiFACndMcd0tatUrt20m+/WWfp475OAAAAAKg6KEoBcFpXXilt2iSNGiUtWiRZLJdfBwAAAADgGihKAXBqdetKb78tBQVdbHv7benIEfNiAgAAAACUH0UpAC5lxQrp73+XQkKkb74xOxoAAAAAQFlRlALgUjp1kq69Vjp5UgoPl2bMYKwpAAAAAHBFFKUAuJSWLaWNG6X775fy8qSYGGnYMCkry+zIAAAAAAClQVEKgMupWVOaP1+aNUvy8JD+8x8pLEz6+WezIwMAAAAA2IuiFACXZLFIY8ZIX30lBQRIu3dLmzebHRUAAAAAwF4eZgcAAOXRs6eUnCx9+ql0771mRwMAAAAAsBd3SgFweU2bStHRF9+nplpn6MvIMC8mAAAAAEDJyn2n1JkzZxQfH69du3bp4MGDSk9Pl5ubmxo2bKhGjRrpmmuu0c0336wmTZpURLwAcFnDh0tffCF9+631Dqq2bc2OCEB1Rq4EAABQtDLfKfXll1/qlltuUWBgoJ577jn98MMPqlOnjtq3b6/27dvLw8NDP/30k15++WU1b95cN9xwg5YvX16RsQNAkZ5/XmrWTDpwQOra1VqYAgBHI1cCAAAomcUwDKM0K6SmpmrEiBHKyclRdHS0brzxRtWvX7/EddLS0rRu3TrNmTNHZ8+e1YIFC9SqVatSBztnzhy98sorSklJUceOHfXGG2+oa9euxfZfsmSJnn32WR06dEht2rTRSy+9pH79+tmWT5kyRR9//LGOHDkiT09PhYSE6IUXXlBoaKhd8WRkZMjX11fp6eny8fEp9fEAqDwnTkiDBlnvlpKkCROk556T3N3NjQuA86qo67qZuZIrI68CAKDqsPe6Xqo7pfbt26chQ4boueeeU0JCgvr373/ZJEuS/Pz8dOedd+p///ufZs2apYceekibSzlN1uLFixUTE6PJkydr+/bt6tixoyIiInTixIki+ycmJmro0KGKiorSjh07FBkZqcjISO3Zs8fW58orr9Ts2bO1e/dubdiwQS1bttStt96qkydPlio2AM6nUSMpPl56/HHr+xdflG67Tfr9d1PDAlDFmZkrAQAAuJpS3Sk1YcIEPfPMM6pdu3a5dnru3Dk999xzeuGFF+TmZl9dLDQ0VF26dNHs2bMlSfn5+QoKCtKYMWM0fvz4S/oPHjxYWVlZWr16ta2tW7du6tSpk+bOnVvkPgoqeV9++aV69+592Zj4Rg9wDYsWSQ89JDVvLm3ZIvGfK4CiVMR13cxcydWRVwEAUHVUyp1SL774YrmTLEmqWbOm4uLi7E6ycnJylJycrPDwcFubm5ubwsPDlZSUVOQ6SUlJhfpLUkRERLH9c3Jy9Pbbb8vX11cdO3a080gAuIJ775WSkqQVKyhIAahcZuVKAAAArqhCMp2cnBzt2LGjIjZVpFOnTikvL08BAQGF2gMCApSSklLkOikpKXb1X716terUqSNvb2/NmDFD8fHx8vf3L3Kb2dnZysjIKPQC4Bo6dpSCgy++f/11aexYKTfXvJgAVB+VnSsBAAC4ogopSv3jH/9Q586d9cILL9jaDh48qH/9619KS0uriF1Umptvvlk7d+5UYmKi+vTpo0GDBhU7TlVcXJx8fX1tr6CgIAdHC6Ai/Pqr9MQT0syZ0i23WAdFB4DK5Mq5EgAAQGWpkKJUQECAXnjhBfXs2dPW1qpVKz3wwAOaOHGifvrpp3Jt39/fX+7u7kpNTS3UnpqaqsDAwCLXCQwMtKt/7dq1dcUVV6hbt25677335OHhoffee6/IbcbGxio9Pd32OnLkSDmOCoBZWrSQPvlEqlvXOjtfSIh1rCkAqCyVnSsBAAC4ogopSl24cEEjR47UDTfcUKi9cePGmjFjht54441ybd/T01MhISFKSEiwteXn5yshIUFhYWFFrhMWFlaovyTFx8cX2//P283Ozi5ymZeXl3x8fAq9ALim/v2thairrpKOHpV69pTefdfsqABUVZWdKwEAALiiCilKTZ48WbfddpseeughLVy4UIcPH7Ytq1GjRoUM0hkTE6N33nlH8+fP1759+/Twww8rKytLI0eOlCQNHz5csbGxtv6PPfaY1q5dq9dee0379+/XlClTtG3bNkVHR0uSsrKyNGHCBG3atEm//vqrkpOT9eCDD+rYsWO65557yh0vAOcXHGwtTEVGSjk50qhR0iOPmB0VgKrIEbkSAACAq/GoiI08+uijqlu3rvbs2aOFCxcqJydHQUFB6t69u7y9vZWZmVnufQwePFgnT57UpEmTlJKSok6dOmnt2rW2wcwPHz5cKKHr3r27Fi1apIkTJ2rChAlq06aNVqx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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
"\n",
"# --------------------------\n",
"# LEFT: trajectory evaluated on f()\n",
"# --------------------------\n",
"ax1.plot(y_list_evaluated, f_list_evaluated, '.--', color='blue')\n",
"ax1.plot(y_list_evaluated, f_list_evaluated, marker='.', color='red',\n",
" linestyle='none', markersize=8,\n",
" label='$\\\\{(y_t,f(y_t))\\\\}_{t=0,\\\\ldots,n} \\\\cup \\\\{(x_n,f(x_n))\\\\}$')\n",
"ax1.plot(xs_evaluated, fs_evaluated, marker='*', color='gold',\n",
" linestyle='none', markersize=8,\n",
" label='$(x_\\\\star,f(x_\\\\star))$')\n",
"\n",
"ax1.set_xlabel('$x$')\n",
"ax1.set_ylabel('$f(x)$')\n",
"ax1.legend()\n",
"ax1.set_title('Trajectory on $f$')\n",
"\n",
"\n",
"# --------------------------\n",
"# RIGHT: trajectory evaluated on h()\n",
"# --------------------------\n",
"ax2.plot(x_list_evaluated, h_list_evaluated, '.--', color='blue')\n",
"ax2.plot(x_list_evaluated, h_list_evaluated, marker='.', color='red',\n",
" linestyle='none', markersize=8,\n",
" label='$\\\\{(x_t,h(x_t))\\\\}_{t=1,\\\\ldots,n}$')\n",
"ax2.plot(xs_evaluated, hs_evaluated, marker='*', color='gold',\n",
" linestyle='none', markersize=8,\n",
" label='$(x_\\\\star,h(x_\\\\star))$')\n",
"\n",
"ax2.set_xlabel('$x$')\n",
"ax2.set_ylabel('$h(x)$')\n",
"ax2.legend()\n",
"ax2.set_title('Trajectory on $h$')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is already quite informative, but arguably not enough. Can we easily recover a pair of functions interpolating through those points? Lets interpolate an example of a worst-case function $F$ by computing the two functions $f$ and $g$ separately, again using the `interpolator` tool, which we instantiate below."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"feval = f.get_interpolator()\n",
"heval = h.get_interpolator()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"50 / 50 grid points computed\r"
]
}
],
"source": [
"# Grid parameters\n",
"nb_pts_grid = 50 \n",
"margin = .2 # plot the interpolated function slightly outside the convex hull of iterates/optimal point\n",
"\n",
"# Create a grid of points where an interpolating function for f() should be computed:\n",
"y_min = np.min([np.min(y_list_evaluated),xs_evaluated])\n",
"y_max = np.max([np.max(y_list_evaluated),xs_evaluated])\n",
"y_test = np.linspace(y_min-margin,y_max+margin,nb_pts_grid)\n",
"\n",
"fy_test = np.zeros(y_test.shape)\n",
"for i in range(len(y_test)):\n",
" fy_test[i] = feval(np.array([y_test[i]]))\n",
" print(f'{i + 1} / {len(y_test)} grid points computed', end='\\r', flush=True)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"50 / 50 grid points computed\r"
]
}
],
"source": [
"# Create a grid of points where an interpolating function for h() should be computed:\n",
"nb_pts_grid = 50\n",
"x_min = np.min([np.min(x_list_evaluated),xs_evaluated])\n",
"x_max = np.max([np.max(x_list_evaluated),xs_evaluated])\n",
"x_test = np.linspace(x_min-margin,x_max+margin,nb_pts_grid)\n",
"\n",
"hx_test = np.zeros(x_test.shape)\n",
"for i in range(len(x_test)):\n",
" hx_test[i] = heval(np.array([x_test[i]]))\n",
" print(f'{i + 1} / {len(x_test)} grid points computed', end='\\r', flush=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The computed worst-case examples are thus as below:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
"\n",
"# --------------------------\n",
"# LEFT: trajectory evaluated on f()\n",
"# --------------------------\n",
"ax1.plot(y_test, fy_test, '--', color='blue')\n",
"ax1.plot(y_list_evaluated, f_list_evaluated, marker='.', color='red',\n",
" linestyle='none', markersize=8,\n",
" label='$\\\\{(y_t,f(y_t))\\\\}_{t=0,\\\\ldots,n} \\\\cup \\\\{(x_n,f(x_n))\\\\}$')\n",
"ax1.plot(xs_evaluated, fs_evaluated, marker='*', color='gold',\n",
" linestyle='none', markersize=8,\n",
" label='$(x_\\\\star,f(x_\\\\star))$')\n",
"\n",
"ax1.set_xlabel('$x$')\n",
"ax1.set_ylabel('$f(x)$')\n",
"ax1.legend()\n",
"ax1.set_title('Trajectory on $f$')\n",
"\n",
"\n",
"# --------------------------\n",
"# RIGHT: trajectory evaluated on h()\n",
"# --------------------------\n",
"ax2.plot(x_test, hx_test, '--', color='blue')\n",
"ax2.plot(x_list_evaluated, h_list_evaluated, marker='.', color='red',\n",
" linestyle='none', markersize=8,\n",
" label='$\\\\{(x_t,h(x_t))\\\\}_{t=1,\\\\ldots,n}$')\n",
"ax2.plot(xs_evaluated, hs_evaluated, marker='*', color='gold',\n",
" linestyle='none', markersize=8,\n",
" label='$(x_\\\\star,h(x_\\\\star))$')\n",
"\n",
"ax2.set_xlabel('$x$')\n",
"ax2.set_ylabel('$h(x)$')\n",
"ax2.legend()\n",
"ax2.set_title('Trajectory on $h$')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we observe that the worst-case is achieved already when $f$ is linear and when $h$ is a $\\ell_1$-shaped (in fact, a simple worst-case example of $h$ is just the indicator function, see, e.g., [this paper (Section 4.2)](https://arxiv.org/pdf/1512.07516) or [Yoel Drori's thesis, Section 2.8](https://www.researchgate.net/profile/Yoel-Drori/publication/303895929_Contributions_to_the_Complexity_Analysis_of_Optimization_Algorithms/links/575b19f008ae9a9c95519686/Contributions-to-the-Complexity-Analysis-of-Optimization-Algorithms.pdf) for the related projected gradient method)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3 : gradient descent for potentially non-convex minimization \n",
"\n",
"We consider the following convex minimization problem:\n",
"\\begin{equation}\n",
"f_\\star \\triangleq \\min_x f(x),\n",
"\\end{equation}\n",
"where $f$ is $L$-smooth (and potentially non-convex).\n",
"\n",
"For this example, we consider the problem of computing the smallest possible $\\tau(n, L, \\mu, \\gamma)$ such that the following guarantee holds (for any initialization of the algorithm, and any $L$-smooth function)\n",
"\\begin{equation}\n",
"\\min_{0\\leq t\\leq n} \\|\\nabla f(x_t)\\|^2 \\leqslant \\tau(n, L, \\gamma) (f(x_0)-f(x_\\star)),\n",
"\\end{equation}\n",
"where $x_t$ are the iterates gradient descent with step size $\\gamma$, started from $x_0$:\n",
"\\begin{equation}\n",
"x_{t+1} = x_t - \\gamma \\nabla f(x_t),\n",
"\\end{equation}\n",
"and where $x_\\star$ is a stationary point such that $f(x_\\star)\\leq f(x_t)$ for all $t=0,1,\\ldots,n$.\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 4 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 1 function(s)\n",
"\t\t\tFunction 1 : Adding 20 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 20 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 1 function(s)\n",
"\t\t\tFunction 1 : Adding 4 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 4 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 6x6\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.37409398278086625\n",
"(PEPit) Postprocessing: 3 eigenvalue(s) > 2.4421028820441136e-07 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.3740929827808663\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 1.69684698132068e-08 after 1 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.3740929827808663\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 0 after 2 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.3740929827808663\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 0 after 3 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.3740929827808663\n",
"(PEPit) Postprocessing: 1 eigenvalue(s) > 0 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -9.78e-11 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 9.78398866358543e-11\n",
"\t\tAll the primal scalar constraints are verified\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative up to an error of 1.7054939895156864e-09\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 1.0227133351078837e-08\n",
"(PEPit) Final upper bound (dual): 0.37409398344859657 and lower bound (primal example): 0.3740929827808663 \n",
"(PEPit) Duality gap: absolute: 1.000667730288729e-06 and relative: 2.6749171365101323e-06\n"
]
}
],
"source": [
"from PEPit import PEP\n",
"from PEPit.functions import SmoothFunction\n",
"\n",
"L = 1\n",
"n = 3\n",
"gamma = .95/L\n",
"verbose = 1\n",
"\n",
"\n",
"# Instantiate PEP\n",
"problem = PEP()\n",
"\n",
"# Declare a smooth strongly convex function\n",
"f = problem.declare_function(SmoothFunction, L=L)\n",
"\n",
"# Then define the starting point x0 of the algorithm as well as corresponding gradient and function value g0 and f0\n",
"x0 = problem.set_initial_point()\n",
"g0, f0 = f.oracle(x0)\n",
"\n",
"xs = f.stationary_point()\n",
"gs, fs = f.oracle(xs)\n",
"\n",
"# Run n steps of GD method with step-size gamma\n",
"x_list = list()\n",
"g_list = list()\n",
"f_list = list()\n",
"gx, fx = g0, f0\n",
"\n",
"x_list.append(x0)\n",
"f_list.append(f0)\n",
"g_list.append(g0)\n",
"\n",
"for i in range(n):\n",
" # Set the performance metric to the minimum of the gradient norm over the iterations\n",
" problem.set_performance_metric(gx**2)\n",
" f.add_constraint(fs <= fx - 1/2/L * gx**2)\n",
" x_list.append(x_list[-1] - gamma * gx)\n",
" gx, fx = f.oracle(x_list[-1])\n",
" f_list.append(fx)\n",
" g_list.append(gx)\n",
"problem.set_performance_metric(gx**2)\n",
"f.add_constraint(fs <= fx - 1/2/L * gx**2)\n",
"\n",
"# Set initial condition\n",
"problem.set_initial_condition( f0 - fs == 1)\n",
"\n",
"# Solve the PEP\n",
"pepit_verbose = max(verbose, 0)\n",
"pepit_tau = problem.solve(verbose=pepit_verbose, dimension_reduction_heuristic=\"logdet3\", tol_dimension_reduction=1e-6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again: PEPit claims to have found a 1D counterexample, so we focus on the first coordinates of the output."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# Evaluate the coordinate, gradient, and function values\n",
"x_list_evaluated = [x.eval()[0] for x in x_list]\n",
"g_list_evaluated = [g.eval()[0] for g in g_list]\n",
"f_list_evaluated = [f.eval() for f in f_list]\n",
"\n",
"# Evaluate a specific point (x*):\n",
"xs_evaluated = xs.eval()[0] # x*\n",
"fs_evaluated = fs.eval() # f(x*)\n",
"gs_evaluated = gs.eval()[0] # g(x*)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now obtain the interpolator and use it to visualize a worst-case instance!"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100 / 100 grid points computed\r"
]
}
],
"source": [
"# get an interpolator\n",
"feval = f.get_interpolator()\n",
"\n",
"\n",
"# Create a grid of points where an interpolating function for f() should be computed:\n",
"nb_pts_grid = 100 # number of points on the grid\n",
"margin = .2 # extrapolate outside only evaluated points\n",
"\n",
"x_min = np.min([np.min(x_list_evaluated),xs_evaluated])\n",
"x_max = np.max([np.max(x_list_evaluated),xs_evaluated])\n",
"x_test = np.linspace(x_min-margin,x_max+margin,nb_pts_grid)\n",
"\n",
"fx_test = np.zeros(x_test.shape)\n",
"# Interpolate on the grid!\n",
"for i in range(len(x_test)):\n",
" fx_test[i] = feval(np.array([x_test[i]]))\n",
" print(f'{i + 1} / {len(x_test)} grid points computed', end='\\r', flush=True)\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x_test, fx_test, '--', color='blue')\n",
"plt.plot(x_list_evaluated, f_list_evaluated, marker='.', color='red', linestyle='none', markersize=8, label=r'$(x_t,f(x_t))$')\n",
"plt.plot(xs_evaluated, fs_evaluated, marker='*', color='gold', linestyle='none', markersize=8, label=r'$(x_\\star,f(x_\\star))$')\n",
"\n",
"\n",
"plt.legend()\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$f(x)$')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A natural question now is whether this interpolator is actually unique. In fact, it is not in general. In PEPit, the default interpolator is often the one that creates the *lowest possible* interpolating function (the one that results in points with the *smallest possible function value*), but one can configure the interpolator to do the opposite (as we shall see in the next example)."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100 / 100 grid points computed\r"
]
}
],
"source": [
"# get an interpolator\n",
"feval = f.get_interpolator(options='highest')\n",
"\n",
"\n",
"# Create a grid of points where an interpolating function for f() should be computed:\n",
"nb_pts_grid = 100 # number of points on the grid\n",
"margin = .2 # extrapolate outside only evaluated points\n",
"\n",
"x_min = np.min([np.min(x_list_evaluated),xs_evaluated])\n",
"x_max = np.max([np.max(x_list_evaluated),xs_evaluated])\n",
"x_test = np.linspace(x_min-margin,x_max+margin,nb_pts_grid)\n",
"\n",
"fx_test = np.zeros(x_test.shape)\n",
"# Interpolate on the grid!\n",
"for i in range(len(x_test)):\n",
" fx_test[i] = feval(np.array([x_test[i]]))\n",
" print(f'{i + 1} / {len(x_test)} grid points computed', end='\\r', flush=True)\n"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"feval_lowest = f.get_interpolator()\n",
"fx_test_lowest = np.array([feval_lowest(np.array([x])) for x in x_test])\n",
"\n",
"plt.plot(x_test, fx_test_lowest, '--', color='blue', label='Lowest interpolating function')\n",
"plt.plot(x_test, fx_test, '--', color='orange', label='Highest interpolating function')\n",
"plt.plot(x_list_evaluated, f_list_evaluated, marker='.', color='red', linestyle='none', markersize=8, label='Shared interpolation points')\n",
"plt.plot(xs_evaluated, fs_evaluated, marker='*', color='gold', linestyle='none', markersize=8, label='Shared stationary point')\n",
"\n",
"\n",
"plt.legend()\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$f(x)$')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is slightly different from the previous example (particularly outside of the range $[x_\\star,x_0]$)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 4 : alternate projections for finding a point in the intersection of two convex sets \n",
"\n",
"In this example, we model the problem of finding a point in the intersection of two convex sets:\n",
"\\begin{equation}\n",
"\\text{Find } x\\in\\mathbb{R}^d: x\\in Q_1\\cap Q_2 \\quad \\Leftrightarrow \\quad \\min_{x\\in\\mathbb{R}^d} f_1(x)+f_2(x),\n",
"\\end{equation}\n",
"with $f_1,f_2$ respectively the indicator functions for $Q_1$ and $Q_2$, which are closed convex sets.\n",
"\n",
"More precisely, we investigate low-dimensional examples achieving a worst-case ratio for the criterion:\n",
"\\begin{equation}\n",
"\\frac{\\|\\mathrm{Proj}_{Q_1}(x_t)-\\mathrm{Proj}_{Q_2}(x_t)\\|^2}{\\|x_0-x_\\star\\|^2}\n",
"\\end{equation}\n",
"\n",
"where $x_t$ ($t\\in\\{0,\\ldots,n\\}$) are generated by the alternate projection method\n",
"\n",
"\\begin{equation}\n",
"x_{t+1} = \\mathrm{Proj}_{Q_2}\\left(\\mathrm{Proj}_{Q_1}\\left(x_t\\right)\\right).\n",
"\\end{equation}\n",
"\n",
"\n",
"We start by importing a few functions."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"from PEPit import PEP\n",
"from PEPit.functions import ConvexIndicatorFunction\n",
"from PEPit.primitive_steps import proximal_step"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 2 function(s)\n",
"\t\t\tFunction 1 : Adding 36 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 36 scalar constraint(s) added\n",
"\t\t\tFunction 2 : Adding 36 scalar constraint(s) ...\n",
"\t\t\tFunction 2 : 36 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 0 function(s)\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 13x13\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.04330493475326395\n",
"(PEPit) Postprocessing: 4 eigenvalue(s) > 1.3104667297245587e-07 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.043204935518465194\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 5.7373804962052685e-09 after 1 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.04320493494675339\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 0 after 2 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.04320493494675339\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 0 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -5.09e-11 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 5.0896326265142404e-11\n",
"\t\tAll the primal scalar constraints are verified up to an error of 4.910116757628202e-11\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 6.498126528869207e-08\n",
"(PEPit) Final upper bound (dual): 0.04330493817018899 and lower bound (primal example): 0.04320493494675339 \n",
"(PEPit) Duality gap: absolute: 0.0001000032234355977 and relative: 0.0023146250204714724\n"
]
}
],
"source": [
"# Parameters / options for the study:\n",
"verbose = 1 # verbose\n",
"n = 5 # number of iterations\n",
"\n",
"\n",
"# Instantiate PEP\n",
"problem = PEP()\n",
"\n",
"f1 = problem.declare_function(ConvexIndicatorFunction) # indicator for Q1\n",
"f2 = problem.declare_function(ConvexIndicatorFunction) # indicator for Q2\n",
"func = f1 + f2 # indicator for the intersection\n",
"\n",
"# x* is a point in the intersection\n",
"xs = func.stationary_point()\n",
"\n",
"# Then define the starting point x0 of the algorithm\n",
"x0 = problem.set_initial_point()\n",
"\n",
"# Run the alternate projection method\n",
"z_list = list() # list of points after projections\n",
"x = x0\n",
"for i in range(n):\n",
" y, _, _ = proximal_step(x, f1, 1)\n",
" z_list.append(y)\n",
" x, _, _ = proximal_step(y, f2, 1)\n",
" z_list.append(x)\n",
"\n",
"# Set the performance metric to the distance between x and xs\n",
"problem.set_performance_metric((y-x)**2)\n",
"problem.set_initial_condition((x0-xs)**2==1)\n",
"\n",
"\n",
"# Solve the PEP\n",
"pepit_tau = problem.solve(verbose=verbose, dimension_reduction_heuristic='logdet2')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As PEPit claims to have found a 2D example, we only visualize the first 2 coordinates of the identified worst-case instance."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"# Evaluation at the optimal point:\n",
"xs_evaluated = xs.eval()[0:2] # x*\n",
"\n",
"# Evaluation of the trajectories (centered around x* = 0 for simplicity)\n",
"z_list_evaluated = [z.eval()[0:2]-xs_evaluated[0:2] for z in z_list] # centered iterates\n",
"\n",
"xs_evaluated = xs_evaluated - xs_evaluated # should be zero "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z = np.array(z_list_evaluated)\n",
"x_points = np.vstack([x0.eval()[0:2] - xs.eval()[0:2], z[1::2]])\n",
"y_points = z[::2]\n",
"x_star = np.zeros(2)\n",
"\n",
"# The worst-case sets are lines: find out their angle from the solution\n",
"q1_dir = y_points[np.argmax(np.sum(y_points**2, axis=1))]\n",
"q1_dir = q1_dir / np.linalg.norm(q1_dir)\n",
"q2_dir = x_points[1:][np.argmax(np.sum(x_points[1:]**2, axis=1))]\n",
"q2_dir = q2_dir / np.linalg.norm(q2_dir)\n",
"\n",
"extent = 1.15 * np.max(np.abs(np.vstack([x_points, y_points, x_star])))\n",
"t = np.linspace(-extent, extent, 200)\n",
"\n",
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"ax.plot(t * q1_dir[0], t * q1_dir[1], '-.', color='tab:orange', lw=2, label=r'$Q_1$')\n",
"ax.plot(t * q2_dir[0], t * q2_dir[1], '--', color='tab:blue', lw=2, label=r'$Q_2$')\n",
"\n",
"steps = [step for k in range(len(y_points))\n",
" for step in ((x_points[k], y_points[k], 'tab:orange'),\n",
" (y_points[k], x_points[k + 1], 'tab:blue'))]\n",
"for i, (start, end, color) in enumerate(steps):\n",
" if not np.allclose(start, end):\n",
" ax.annotate('', xy=end, xytext=start,\n",
" arrowprops=dict(arrowstyle='-|>', color=color, lw=1.8, mutation_scale=12,\n",
" shrinkA=0, shrinkB=4),\n",
" zorder=len(steps) - i)\n",
"\n",
"y_plot = y_points[1:] if np.allclose(y_points[0], x_points[0]) else y_points\n",
"ax.scatter(x_points[1:, 0], x_points[1:, 1], color='tab:blue', s=60, edgecolors='black', linewidths=0.8, label=r'$x_t$', zorder=20)\n",
"ax.scatter(y_plot[:, 0], y_plot[:, 1], color='tab:orange', s=60, edgecolors='black', linewidths=0.8, label=r'$y_t$', zorder=20)\n",
"ax.scatter(*x_points[0], marker='s', color='green', s=120, edgecolors='black', linewidths=1.0, label=r'$x_0$', zorder=21)\n",
"ax.scatter(*x_star, marker='*', color='gold', s=220, edgecolors='goldenrod', linewidths=1.0, label=r'$x_\\star$', zorder=21)\n",
"\n",
"ax.set_xlabel('$z_1$')\n",
"ax.set_ylabel('$z_2$')\n",
"ax.set_aspect('equal', adjustable='box')\n",
"ax.legend()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We observe a nice alternate projection between two hyperplanes! (and tuning the angle between the hyperplanes suffices to obtain the worst-case estimate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 5 : primal-dual proximal point for convex minimization \n",
"\n",
"For this last example, we consider again the problem of minimizing a sum:\n",
"\\begin{equation}\n",
"\\min_{x\\in\\mathbb{R}^d} f(x)+h(x)\n",
"\\end{equation}\n",
"where both $f$ and $h$ are closed convex and proper, and we assume $\\exists x_\\star,y_\\star$ (KKT point): $-y_\\star\\in\\partial f(x_\\star),\\, x_\\star\\in\\partial h^*(y_\\star)$.\n",
" \n",
"We study the primal-dual (PD) proximal-point algorithm for solving such problems: \n",
"\\begin{align}\n",
"(y_{k+1},x_{k+1})=\\underset{y\\in\\mathbb{R}^d}{\\mathrm{argmax}}\\,\\,\\underset{x\\in\\mathbb{R}^d}{\\mathrm{argmin}} \\Bigl\\{f(x)-h^*(y)+\\langle y,\\, x\\rangle +\\tfrac1{2\\alpha} \\|x-x_k\\|^2-\\tfrac1{2\\alpha} \\|y-y_k\\|^2 \\Bigl\\}\n",
"\\end{align}\n",
"and we inspect guarantees of the form (for some elements of $\\partial f$ and $\\partial h^*$)\n",
"\\begin{equation}\n",
"\\frac{\\|g_N+y_N\\|^2 + \\|x_N-s_N\\|^2}{\\|x_0 - x_\\star\\|^2+\\|y_0-y_\\star\\|^2}\\leq \\tau(N,\\alpha)\n",
"\\end{equation}\n",
"with $g_N\\in\\partial f(x_N)$ and $s_N\\in\\partial h^*(y_N)$.\n",
"\n",
"To study this algorithm, we first import some necessary functions, followed by an implementation of the primal-dual proximal step in PEPit:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"from PEPit import PEP\n",
"from PEPit.point import Point\n",
"from PEPit.expression import Expression\n",
"from PEPit.functions import ConvexFunction\n",
"import numpy as np\n",
"\n",
"def PD_proximal_step(x0,lambda0, f, g, alpha):\n",
" x1 = Point()\n",
" lambda1 = Point()\n",
" \n",
" # subgradients\n",
" pf_x1 = (x0-x1)/alpha-lambda1\n",
" pg_lambda1 = (lambda0-lambda1)/alpha+x1\n",
" \n",
" fx1 = Expression()\n",
" glambda1 = Expression()\n",
" \n",
" f.add_point((x1, pf_x1, fx1))\n",
" g.add_point((pg_lambda1, lambda1, glambda1))\n",
"\n",
" return x1, lambda1, pf_x1, pg_lambda1\n",
"\n",
"# helper function: evaluation of conjugate\n",
"def evaluate_conjugate(lam,f):\n",
" x = Point()\n",
" fx = Expression()\n",
" f.add_point((x, lam, fx))\n",
" fconj = lam*x - fx\n",
" return fconj"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 2 function(s)\n",
"\t\t\tFunction 1 : Adding 420 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 420 scalar constraint(s) added\n",
"\t\t\tFunction 2 : Adding 420 scalar constraint(s) ...\n",
"\t\t\tFunction 2 : 420 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 0 function(s)\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 44x44\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.018867672516958034\n",
"(PEPit) Postprocessing: 6 eigenvalue(s) > 9.271131793728988e-08 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.01876767204806424\n",
"(PEPit) Postprocessing: 3 eigenvalue(s) > 0.005870284881130875 after 1 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.018767672468967378\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 2.076211886853175e-11 after 2 dimension reduction step(s)\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.018767672468967378\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 2.076211886853175e-11 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -8.13e-11 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 8.129860241260612e-11\n",
"\t\tAll the primal scalar constraints are verified up to an error of 1.729408734274518e-10\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 3.191634905460896e-08\n",
"(PEPit) Final upper bound (dual): 0.018867673113931446 and lower bound (primal example): 0.018767672468967378 \n",
"(PEPit) Duality gap: absolute: 0.00010000064496406766 and relative: 0.005328345596899146\n"
]
}
],
"source": [
"n = 20 # number of iterations\n",
"alpha = n * [1] # step sizes\n",
"verbose = 1 # verbose mode\n",
"\n",
"\n",
"# PEP:\n",
"problem = PEP()\n",
"\n",
"# Problem setup\n",
"f = problem.declare_function(ConvexFunction, reuse_gradient=True)\n",
"g = problem.declare_function(ConvexFunction, reuse_gradient=True)\n",
"F = f+g\n",
"\n",
"# Optimal primal and dual solutions\n",
"xs = F.stationary_point()\n",
"ys = -f.gradient(xs)\n",
"\n",
"# Starting point of the algorithm\n",
"x0 = problem.set_initial_point()\n",
"y0 = problem.set_initial_point()\n",
"\n",
"\n",
"# Compute n steps of the proximal method starting from x0\n",
"x_list = list()\n",
"y_list = list()\n",
"x_list.append(x0)\n",
"y_list.append(y0)\n",
"\n",
"x = x0\n",
"y = y0\n",
"for i in range(n):\n",
" x, y, df_xk, dg_lambdak = PD_proximal_step(x, y, f, g, alpha[i])\n",
" x_list.append(x)\n",
" y_list.append(y)\n",
"\n",
"# Set initial condition (distance to a solution)\n",
"problem.set_initial_condition((x0 - xs) ** 2 + (y0 - ys) ** 2 <= 1)\n",
"\n",
"# Set performance metric: KKT residual\n",
"problem.set_performance_metric((df_xk+y) ** 2 + (x - dg_lambdak) ** 2)\n",
"\n",
"# Solve the PEP\n",
"pepit_tau = problem.solve(verbose=verbose, dimension_reduction_heuristic=\"logdet2\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PEPit claims to have found a 2D counter-example, so let us only visualize the first two coordinates."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"# Evaluate specific point (a solution)\n",
"xs_evaluated = xs.eval()[0:2] # x*\n",
"ys_evaluated = ys.eval()[0:2] # y*\n",
"\n",
"# Evaluate the list of iterates (centered around the solution above, for simplificty)\n",
"x_list_evaluated = [x.eval()[0:2]-xs_evaluated for x in x_list] # centered iterates\n",
"xs_evaluated = xs_evaluated - xs_evaluated # should be zero \n",
"y_list_evaluated = [y.eval()[0:2]-ys_evaluated for y in y_list] # centered iterates\n",
"ys_evaluated = ys_evaluated - ys_evaluated # should be zero "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let us plot a worst-case trajectory!"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "355905dd306d445f8111e7f8e3451421",
"version_major": 2,
"version_minor": 0
},
"image/png": 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",
"text/html": [
"\n",
"
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"
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" Figure\n",
"
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" \n",
"
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" "
],
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib widget\n",
"plt.ion() # <-- this enables rotation\n",
"\n",
"\n",
"import numpy as np\n",
"\n",
"# Convert the list of 2D vectors into two arrays x1, x2\n",
"x_array = np.array(x_list_evaluated) \n",
"x1 = x_array[:, 0]\n",
"x2 = x_array[:, 1]\n",
"# Convert the list of 2D vectors into two arrays y1, y2\n",
"y_array = np.array(y_list_evaluated)\n",
"y1 = y_array[:, 0]\n",
"y2 = y_array[:, 1]\n",
"\n",
"# Worst-case point (xs_evaluated is a 2D vector)\n",
"xs = np.array(xs_evaluated)\n",
"xs1, xs2 = xs[0], xs[1]\n",
"# Worst-case point (ys_evaluated is a 2D vector)\n",
"ys = np.array(ys_evaluated)\n",
"ys1, ys2 = ys[0], ys[1]\n",
"\n",
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"\n",
"# Blue line (trajectory)\n",
"ax.plot(x1, y1, y2, '--', color='blue')\n",
"ax.scatter(x1, y1, y2, marker='o', color='red',\n",
" s=20, label='$(x_t,y_t^{(1)},y_t^{(2)})$')\n",
"\n",
"# Gold star (optimal point)\n",
"ax.scatter(xs1, ys1, ys2, marker='*', color='gold',\n",
" s=100, label=r'$(x_\\star,y_\\star^{(1)},y_\\star^{(2)})$')\n",
"\n",
"# Green point (starting point)\n",
"ax.scatter(x1[0], y1[0], y2[0], marker='s', color='green',\n",
" s=100, label='$(x_0,y_0^{(1)},y_0^{(2)})$')\n",
"\n",
"ax.set_xlabel('$x^{(1)}$')\n",
"ax.set_ylabel('$y^{(1)}$')\n",
"ax.set_zlabel('$y^{(2)}$')\n",
"\n",
"ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.08), ncol=3, borderaxespad=0.)\n",
"fig.subplots_adjust(bottom=0.2)\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6 : gradient descent with exact line-search \n",
"\n",
"We now consider the problem of finding:\n",
"\\begin{equation}\n",
"f_\\star \\triangleq \\min_x f(x),\n",
"\\end{equation}\n",
"where $f$ is $L$-smooth and $\\mu$-strongly convex.\n",
"\n",
"For this example, we consider the problem of computing the smallest possible $\\tau(n, L, \\gamma)$ such that the following guarantee holds (for any initialization of the algorithm, and any $L$-smooth and $\\mu$-strognly convex functions)\n",
"\\begin{equation}\n",
"f(x_n)-f_\\star \\leqslant \\tau(n, L, \\mu) \\| x_0 - x_\\star \\|^2,\n",
"\\end{equation}\n",
"where $x_n$ is the output of gradient descent using the per-iteration optimal step size $\\gamma_k = \\arg\\min_\\gamma f(x_k) - \\gamma \\cdot \\nabla f(x_k)$, started from $x_0$, and where $x_\\star$ is the minimizer of $f$."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(PEPit) Setting up the problem: performance measure is the minimum of 1 element(s)\n",
"(PEPit) Setting up the problem: Adding initial conditions and general constraints ...\n",
"(PEPit) Setting up the problem: initial conditions and general constraints (1 constraint(s) added)\n",
"(PEPit) Setting up the problem: interpolation conditions for 1 function(s)\n",
"\t\t\tFunction 1 : Adding 42 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 42 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: additional constraints for 1 function(s)\n",
"\t\t\tFunction 1 : Adding 10 scalar constraint(s) ...\n",
"\t\t\tFunction 1 : 10 scalar constraint(s) added\n",
"(PEPit) Setting up the problem: size of the Gram matrix: 13x13\n",
"(PEPit) Compiling SDP\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (wrapper:cvxpy, solver: MOSEK); optimal value: 0.1344305389387117\n",
"(PEPit) Postprocessing: 3 eigenvalue(s) > 5.4073880114545966e-06 before dimension reduction\n",
"(PEPit) Calling SDP solver\n",
"(PEPit) Solver status: optimal (solver: MOSEK); objective value: 0.13433053869743988\n",
"(PEPit) Postprocessing: 2 eigenvalue(s) > 6.004102165538769e-08 after dimension reduction\n",
"\u001b[96m(PEPit) Postprocessing: solver's output is not entirely feasible (smallest eigenvalue of the Gram matrix is: -2.31e-10 < 0).\n",
" Small deviation from 0 may simply be due to numerical error. Big ones should be deeply investigated.\n",
" In any case, from now the provided values of parameters are based on the projection of the Gram matrix onto the cone of symmetric semi-definite matrix.\u001b[0m\n",
"(PEPit) Primal feasibility check:\n",
"\t\tThe solver found a Gram matrix that is positive semi-definite up to an error of 2.3052389346073744e-10\n",
"\t\tAll the primal scalar constraints are verified up to an error of 3.7212867856628584e-10\n",
"(PEPit) Dual feasibility check:\n",
"\t\tThe solver found a residual matrix that is positive semi-definite\n",
"\t\tAll the dual scalar values associated with inequality constraints are nonnegative\n",
"(PEPit) The worst-case guarantee proof is perfectly reconstituted up to an error of 1.411303044625698e-07\n",
"(PEPit) Final upper bound (dual): 0.13443054662214557 and lower bound (primal example): 0.13433053869743988 \n",
"(PEPit) Duality gap: absolute: 0.0001000079247056862 and relative: 0.0007444913545008525\n"
]
}
],
"source": [
"from PEPit import PEP\n",
"from PEPit.functions import SmoothStronglyConvexFunction\n",
"from PEPit.primitive_steps import exact_linesearch_step\n",
"\n",
"L, mu = 1, .1\n",
"verbose = 1\n",
"n = 5\n",
"\n",
"# Instantiate PEP\n",
"problem = PEP()\n",
"\n",
"# Declare a smooth strongly convex function\n",
"f = problem.declare_function(SmoothStronglyConvexFunction, mu=mu, L=L)\n",
"\n",
"# Start by defining its unique optimal point xs = x_* and corresponding function value fs = f_*\n",
"xs = f.stationary_point()\n",
"gs, fs = f.oracle(xs)\n",
"\n",
"# Then define the starting point x0 of the algorithm as well as corresponding gradient and function value g0 and f0\n",
"x0 = problem.set_initial_point()\n",
"g0, f0 = f.oracle(x0)\n",
"\n",
"# Set the initial constraint that is the difference between f0 and f_*\n",
"problem.set_initial_condition(f0 - fs <= 1)\n",
"\n",
"# Run n steps of GD method with ELS\n",
"x_list = list()\n",
"x_list.append(x0)\n",
"g_list = list()\n",
"g_list.append(g0)\n",
"f_list = list()\n",
"f_list.append(f0)\n",
"\n",
"x = x0\n",
"gx = g0\n",
"for i in range(n):\n",
" x, gx, fx = exact_linesearch_step(x, f, [gx])\n",
" x_list.append(x)\n",
" g_list.append(gx)\n",
" f_list.append(fx)\n",
"\n",
"# Set the performance metric to the function value accuracy\n",
"problem.set_performance_metric(fx - fs)\n",
"\n",
"# Solve the PEP\n",
"pepit_verbose = max(verbose, 0)\n",
"pepit_tau = problem.solve(verbose=pepit_verbose, dimension_reduction_heuristic='trace')\n",
"\n",
"# Compute theoretical guarantee (for comparison)\n",
"theoretical_tau = ((L - mu) / (L + mu)) ** (2 * n)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As before, PEPit claims to have identified a 2D example. So we will focus on the first coordinates of the output vectors."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"xs_evaluated = xs.eval()[0:2] # x*\n",
"gs_evaluated = gs.eval()[0:2] # g(x*)=0\n",
"fs_evaluated = fs.eval() # f(x*)\n",
"\n",
"x_list_evaluated = [x.eval()[0:2] for x in x_list] # iterates\n",
"g_list_evaluated = [g.eval()[0:2] for g in g_list] # gradient values\n",
"f_list_evaluated = [f.eval() for f in f_list] # function values\n",
"\n",
"x_list_evaluated.append(xs_evaluated)\n",
"g_list_evaluated.append(gs_evaluated)\n",
"f_list_evaluated.append(fs_evaluated)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We get the interpolator and interpolate on a grid:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"400 / 400 mesh points computed\r"
]
}
],
"source": [
"feval = f.get_interpolator()\n",
"\n",
"# Create a grid of points where an interpolating function for f() should be computed:\n",
"nb_pts_grid = 20 # number of points on the grid\n",
"margin = .2 # extrapolate outside only evaluated points\n",
"\n",
"# x_list_evaluated is a list of numpy arrays\n",
"first_coordinate = np.array([arr[0] for arr in x_list_evaluated])\n",
"second_coordinate = np.array([arr[1] for arr in x_list_evaluated])\n",
"\n",
"x_min, x_max = np.min(first_coordinate)-margin, np.max(first_coordinate)+margin\n",
"y_min, y_max = np.min(second_coordinate)-margin, np.max(second_coordinate)+margin\n",
"\n",
"# Create test points\n",
"x_test = np.linspace(x_min, x_max, nb_pts_grid)\n",
"y_test = np.linspace(y_min, y_max, nb_pts_grid)\n",
"\n",
"# Create 2D mesh\n",
"X, Y = np.meshgrid(x_test, y_test)\n",
"\n",
"# Array to store function evaluations\n",
"FX = np.zeros(X.shape)\n",
"\n",
"# Loop over the mesh\n",
"for i in range(X.shape[0]):\n",
" for j in range(X.shape[1]):\n",
" x_tested = np.zeros((7,))\n",
" x_tested[0] = X[i, j]\n",
" x_tested[1] = Y[i, j]\n",
" FX[i, j] = feval(x_tested)\n",
"\n",
" print(f'{i * X.shape[1] + j + 1} / {X.size} mesh points computed', end='\\r', flush=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let us plot the function; first with a contour plot (a bit more readable), then followed by a surface plot."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "73e3ac9232ff4f35a20cdb04dc5e7967",
"version_major": 2,
"version_minor": 0
},
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",
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