Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

TL;DR

This paper introduces a modified BFGS algorithm for nonconvex multiobjective optimization that guarantees global convergence and superlinear convergence, with practical efficiency demonstrated through numerical results.

Contribution

It presents a novel BFGS-type algorithm that ensures convergence without convexity assumptions and maintains efficiency in nonconvex multiobjective problems.

Findings

The algorithm achieves global convergence in nonconvex settings.

Superlinear convergence is established under standard conditions.

Numerical experiments confirm the practical effectiveness of the modifications.

Abstract

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration to address the lack of convexity assumption. Numerical results shows that the introduced modifications preserve the practical efficiency of the BFGS method.