Performance Estimation for Weakly Convex Functions

Written for ECE 285 with professor Yang Zheng. Source code can be accessed here. If the pdf fails to load below, the report can be downloaded here.

I analyzed the worst-case performance of first-order methods on nonsmooth weakly convex functions using the performance estimation framework. Lacking exact interpolation conditions, I implemented a relaxation using the necessary conditions for weak convexity and obtained (not necessarily tight) upper bounds on the worst-case performance. The semidefinite program instances were modeled using YALMIP and solved with MOSEK, and the design was left to me. The image below shows the worst-case performance of different step sizes over a fixed number of iterations.