Diminishing Stepsize Methods for Nonconvex Composite Problems via Ghost Penalties: from the General to the Convex Regular Constrained Case

TL;DR

This paper extends diminishing stepsize methods to nonconvex constrained problems with composite objectives, and simplifies the approach for convex constraints, reducing computational complexity.

Contribution

It introduces a generalized diminishing stepsize algorithm for nonconvex composite problems with equality constraints and simplifies it for convex constraints under standard qualification.

Findings

Extended the method to equality constraints and nonsmooth objectives

Simplified the algorithm for convex constraints, reducing computational burden

Demonstrated effectiveness in nonconvex and convex constrained settings

Abstract

In this paper we first extend the diminishing stepsize method for nonconvex constrained problems presented in [4] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case in which the constraints are convex and satisfy a standard constraint qualification and show that in this setting the algorithm can be considerably simplified, reducing the computational burden of each iteration.