Title: Perturbed Proximal Descent to Escape Saddle Points for Non-convex and Non-smooth Objective Functions,
Abstract: We consider the problem of finding local minimizers in non-convex and
non-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 different analysis and a
different algorithm.