Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients

TL;DR

This paper introduces a novel multi-objective optimization algorithm that combines surrogate models, trust-region, and filter methods to effectively handle nonlinear constraints with inexact gradient information, ensuring convergence to optimality.

Contribution

It develops a new derivative-free trust-region filter method for multi-objective problems using fully linear models and addresses gradient inexactness within this framework.

Findings

Proves convergence of a subset of iterates to a quasi-stationary point.

Establishes conditions under which limit points are KKT points.

Demonstrates the method's effectiveness under standard assumptions.

Abstract

In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed, and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem.