Fast Accelerated Proximal Gradient Method with New Extrapolation Term for Multiobjective Optimization

TL;DR

This paper introduces a new accelerated proximal gradient method with an innovative extrapolation scheme for multiobjective optimization, achieving sublinear convergence and demonstrating practical effectiveness through numerical experiments.

Contribution

It proposes a novel extrapolation coefficient scheme within an accelerated proximal gradient algorithm for multiobjective optimization, with proven convergence properties.

Findings

Achieves sublinear convergence rate

Effective in practical numerical experiments

Requires only mild initial conditions for Lipschitz estimate

Abstract

In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed scheme only requires the Lipschitz constant estimate sequence to satisfy mild initial conditions, under which a key equality property can be derived to support the convergence analysis. Numerical experiments are provided to demonstrate the effectiveness and practical performance of the proposed method.