Benchmark of Some Nonsmooth Optimization Solvers for Computing Nonconvex Proximal Points

The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. We then compare the effectiveness of four algorithms (“CProx,” “N1CV2,” “N2FC1,” and “RGS”) in computing the proximal points of such test functions. We also examine two versions of the CProx code to investigate (numerically) if the removal of a “unique proximal point assurance” subroutine allows for improvement in performance when the proximal point is not unique.