---
_id: '33150'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Manuel Bastian
  full_name: Berkemeier, Manuel Bastian
  id: '51701'
  last_name: Berkemeier
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear
    Constraints using Inexact Gradients. <i>arXiv:220812094</i>. Published online
    2022.
  apa: Berkemeier, M. B., &#38; Peitz, S. (2022). Multi-Objective Trust-Region Filter
    Method for Nonlinear Constraints using Inexact Gradients. In <i>arXiv:2208.12094</i>.
  bibtex: '@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter
    Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094},
    author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }'
  chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
    Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>,
    2022.
  ieee: M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method
    for Nonlinear Constraints using Inexact Gradients,” <i>arXiv:2208.12094</i>. 2022.
  mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
    Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>,
    2022.
  short: M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).
date_created: 2022-08-26T06:08:06Z
date_updated: 2022-08-26T06:12:10Z
department:
- _id: '101'
- _id: '655'
external_id:
  arxiv:
  - '2208.12094'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2208.12094
oa: '1'
publication: arXiv:2208.12094
status: public
title: Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using
  Inexact Gradients
type: preprint
user_id: '47427'
year: '2022'
...