Perturbed Proximal Descent to Escape Saddle Points for Non-convex and Non-smooth Objective Functions

We consider the problem of finding local minimizers in nonconvex andnon-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires differentanalysis and a different algorithm. This is the extended version of the paper that contains the proofs.