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

arXiv: https://arxiv.org/abs/2208.12094 · HTML: https://mlsanity.com/paper/2208.12094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Common pitfalls to avoid while using multiobjective optimization in machine learning](https://mlsanity.com/paper/2405.01480/) (2024)

## Abstract (arXiv)

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.