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arXiv · 2208.12094

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

Manuel Berkemeier·Sebastian Peitz
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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.

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Manuel Berkemeier, Sebastian Peitz. 2022-08-25. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. https://arxiv.org/abs/2208.12094

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