Memory gradient method for multiobjective optimization

TL;DR

This paper introduces a novel multiobjective memory gradient method that combines current and past information to efficiently find Pareto critical points, with proven convergence and demonstrated effectiveness through experiments.

Contribution

It presents a new descent method for multiobjective optimization that incorporates memory of past steps, with theoretical convergence guarantees.

Findings

Method converges globally under mild assumptions

Achieves favorable convergence rates

Computational experiments confirm effectiveness

Abstract

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the current descent direction and past multi-step iterative information as a new search direction and to obtain a stepsize by virtue of two types of strategies. It is proved that the developed direction with suitable parameters always satisfies the sufficient descent condition at each iteration. Based on mild assumptions, we obtain the global convergence and the rates of convergence for our method. Computational experiments are given to demonstrate the effectiveness of the proposed method.