1. What’s new in PEPit 0.1.0

  • Adding general constraints to your problem.

    The method add_constraint has been added to the class PEP for general constraints not necessarily related to a specific function.
    For readability of your code, we suggest to use the method set_initial_condition when the constraint is the initial one, and the method add_constraint for any other constraint.

  • Adding LMI constraints to your problem.

    The method add_psd_matrix has been added to the class PEP and must be used to add LMI constraints to your problem.

  • CVXPY options.

    PEPit uses CVXPY to solve the underlying SDP of your problem.
    CVXPY solver options can be provided to the method PEP.solve.

  • Optimizing dimension of the solution.

    The tracetrick option of the method PEP.solve has been replaced by dimension_reduction_heuristic.
    Set to None by default, this option can be set to “trace” or “logdet{followed by a number}” to use one of those heuristic.

  • Granularity of the verbose mode has evolved.

    The verbose mode of the method PEP.solve and of the provided examples files are now integers:

    • 0: No verbose at all

    • 1: PEPit information is printed but not CVXPY’s

    • 2: Both PEPit and CVXPY details are printed

  • Parameters of function classes.

    The parameters that characterize a function class must be provided directly as arguments of this function class, not through the dict “param” anymore.
    Example: PEP.declare_function(function_class=SmoothStronglyConvexFunction, mu=.1, L=1.)

  • Initializing a Point or an Expression to 0.

    null_point and null_expression have been added to the module PEPit to facilitate the access to a Point or an Expression initialized to 0.

  • 3 new function classes have been added:

    • ConvexSupportFunction for convex support functions (see [1])

    • ConvexQGFunction, for convex and quadratically upper bounded functions (see [2])

    • RsiEbFunction, for functions verifying lower restricted secant inequality and upper error bound (see [3])

[1] A. Taylor, J. Hendrickx, F. Glineur (2017). Exact worst-case performance of first-order methods for composite convex optimization. SIAM Journal on Optimization, 27(3):1283–1313.

[2] B. Goujaud, A. Taylor, A. Dieuleveut (2022). Optimal first-order methods for convex functions with a quadratic upper bound.

[3] C. Guille-Escuret, B. Goujaud, A. Ibrahim, I. Mitliagkas (2022). Gradient Descent Is Optimal Under Lower Restricted Secant Inequality And Upper Error Bound. arXiv 2203.00342.