Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

TL;DR

This paper extends integral global optimality conditions to multiobjective problems, introducing an algorithm to approximate the weak Pareto front, demonstrated through numerical tests.

Contribution

It develops integral optimality conditions for non-differentiable multiobjective problems and proposes a new algorithm based on Chebyshev scalarization.

Findings

Effective approximation of the weak Pareto front

Successful application to test problems

Extension of known conditions to multiobjective context

Abstract

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems.