A FISTA-Type First Order Algorithm on Composite Optimization Problems that is Adaptable to the Convex Situation

TL;DR

This paper introduces VAR-FISTA, a flexible first-order algorithm for composite optimization that adapts to convexity, achieving improved iteration complexity in convex cases while maintaining competitive performance.

Contribution

The paper presents VAR-FISTA, a novel FISTA-type algorithm that exploits convexity to enhance iteration complexity in composite optimization problems.

Findings

Achieves improved iteration complexity for convex functions.

Maintains compatibility with best known results for nonconvex functions.

Demonstrates adaptability of the algorithm to different convexity settings.

Abstract

In this note, we propose a FISTA-type first order algorithm, VAR-FISTA, to solve a composite optimization problem. A distinctive feature of VAR-FISTA is its ability to exploit the convexity of the function in the problem, resulting in an improved iteration complexity when the function is convex compared to when it is nonconvex. The iteration complexity result for the convex and nonconvex case obtained in the note are compatible to the best known in the literature so far.