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

01/24/2019

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by   Zhishen Huang, et al.

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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.