The Quasi-Newton Method for the Composite Multiobjective Optimization Problems

TL;DR

This paper develops new quasi-Newton algorithms with Armijo line search for solving composite multiobjective optimization problems, ensuring convergence to Pareto stationary and optimal points under certain conditions.

Contribution

It introduces several novel quasi-Newton methods tailored for CMOPs, expanding the toolkit for multiobjective optimization with convergence guarantees.

Findings

Algorithms generate sequences with accumulation points that are Pareto stationary.

Under suitable conditions, accumulation points are Pareto optimal.

The methods incorporate BFGS, self-scaling BFGS, and Huang BFGS variants.

Abstract

In this paper, we introduce several new quasi-Newton methods for the composite multiobjective optimization problems (in short, CMOP) with Armijo line search. These multiobjective versions of quasi-Newton methods include BFGS quasi-Newnon method, self-scaling BFGS quasi-Newnon method, and Huang BFGS quasi-Newnon method. Under some suitable conditions, we show that each accumulation point of the sequence generated by these algorithms, if exists, is both a Pareto stationary point and a Pareto optimal point of (CMOP).