A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems

TL;DR

This paper introduces a descent method for constrained multiobjective optimization problems that extends existing unconstrained methods by incorporating active set strategies, ensuring convergence to Pareto optimal points.

Contribution

It generalizes the steepest descent method to handle equality and inequality constraints in multiobjective problems using active set strategies.

Findings

Accumulation points satisfy necessary conditions for local Pareto optimality.

The method demonstrates typical behavior in a numerical example.

Abstract

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.