PEPit.primitive_steps.linear_optimization_step
- PEPit.primitive_steps.linear_optimization_step(dir, ind)[source]
This routine outputs the result of a minimization problem with linear objective (whose direction is provided by dir) on the domain of the (closed convex) indicator function ind. That is, it outputs a solution to
\[\arg\min_{\text{ind}(x)=0} \left< \text{dir};\, x \right>,\]One can notice that \(x\) is solution of this problem if and only if
\[- \text{dir} \in \partial \text{ind}(x).\]- Parameters
dir (Point) – direction of optimization
ind (ConvexIndicatorFunction) – convex indicator function
- Returns
x (Point) – the optimal point.
gx (Point) – the (sub)gradient of ind on x.
fx (Expression) – the function value of ind on x.