Convergence of a Stochastic Subgradient Method with Averaging for Nonsmooth Nonconvex Constrained Optimization

TL;DR

This paper proves the convergence of a stochastic subgradient method with averaging for nonsmooth, nonconvex constrained optimization problems, introducing a chain rule for generalized differentiability functions.

Contribution

It establishes convergence results for a single time-scale stochastic subgradient method with averaging in nonsmooth, nonconvex constrained settings, and proves a new chain rule for such functions.

Findings

Convergence of the proposed method is theoretically guaranteed.

A chain rule for generalized differentiability functions is established.

The analysis applies to constrained nonsmooth, nonconvex optimization problems.

Abstract

We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool of our analysis, we also prove a chain rule on a path for such functions.