A proximal method for composite minimization

TL;DR

This paper introduces a proximal method for minimizing composite functions, combining linearized approximations and regularization, with proven convergence properties and promising initial computational results for both convex and nonconvex problems.

Contribution

It proposes a novel proximal algorithm framework for composite minimization problems involving convex or prox-regular functions, with theoretical convergence guarantees.

Findings

Global convergence established for the proposed method

Active manifold identification property proven

Preliminary computational results show promising performance

Abstract

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational results on both convex and nonconvex examples are promising.