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

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.

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References in corpus (4)

• Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization
• A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems
• A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems
• An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems