Faster FISTA

TL;DR

This paper introduces a simple modification to FISTA that guarantees convergence and improves practical performance, addressing oscillatory issues observed in the original algorithm.

Contribution

A novel modification to FISTA that ensures convergence and enhances practical efficiency, supported by theoretical proof and empirical results.

Findings

Proven convergence of the modified FISTA.

Superior practical performance over original FISTA.

Numerical experiments demonstrating improved results.

Abstract

The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its performance is not as desired owing to the (local) oscillatory behaviour. Over the years, various approaches are proposed to overcome this drawback of FISTA, in this paper, we propose a simple yet effective modification to the algorithm which has two advantages: 1) it enables us to prove the convergence of the generated sequence; 2) it shows superior practical performance compared to the original FISTA. Numerical experiments are presented to illustrate the superior performance of the proposed algorithm.