PRP, HS and LS Conjugate Gradient Methods for Interval-Valued Multiobjective Optimization Problems

TL;DR

This paper introduces conjugate gradient algorithms tailored for interval-valued multiobjective optimization, utilizing Wolfe line search and proving global convergence, with numerical tests confirming their effectiveness.

Contribution

Develops three variants of conjugate gradient methods with Wolfe line search for interval multiobjective problems, establishing their convergence and demonstrating superior performance.

Findings

Algorithms successfully compute Pareto critical points.

Global convergence of the methods is rigorously proven.

Numerical experiments show improved efficiency on benchmark problems.

Abstract

In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story schemes for computing Pareto critical points in unconstrained interval-valued multiobjective optimization problems. The proposed algorithm incorporates a Wolfe line search strategy to determine a suitable range of step size that satisfies the standard Wolfe conditions. For each of the proposed variants of the nonlinear conjugate gradient method, we establish rigorous global convergence results under appropriate assumptions. To demonstrate the effectiveness of the proposed methods, we conduct numerical experiments on a set of benchmark test problems and present a comprehensive performance profile analysis.