---
_id: '21337'
abstract:
- lang: eng
  text: "We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly
    constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous
    and expensive problems, i.e., problems that have at least one\r\nobjective function
    that is computationally expensive. The method is\r\nderivative-free in the sense
    that neither need derivative information be\r\navailable for the expensive objectives
    nor are gradients approximated using\r\nrepeated function evaluations as is the
    case in finite-difference methods.\r\nInstead, a multiobjective trust region approach
    is used that works similarly to\r\nits well-known scalar pendants. Local surrogate
    models constructed from\r\nevaluation data of the true objective functions are
    employed to compute\r\npossible descent directions. In contrast to existing multiobjective
    trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed
    radial basis function networks. This has the important advantage\r\nthat the number
    of data points scales linearly with the parameter space\r\ndimension. The local
    models qualify as fully linear and the corresponding\r\ngeneral scalar framework
    is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical
    points is proven and numerical examples\r\nillustrate our findings."
article_number: '31'
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. Derivative-Free Multiobjective Trust Region Descent
    Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational
    Applications</i>. 2021;26(2). doi:<a href="https://doi.org/10.3390/mca26020031">10.3390/mca26020031</a>
  apa: Berkemeier, M. B., &#38; Peitz, S. (2021). Derivative-Free Multiobjective Trust
    Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical
    and Computational Applications</i>, <i>26</i>(2). <a href="https://doi.org/10.3390/mca26020031">https://doi.org/10.3390/mca26020031</a>
  bibtex: '@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust
    Region Descent Method Using Radial  Basis Function Surrogate Models}, volume={26},
    DOI={<a href="https://doi.org/10.3390/mca26020031">10.3390/mca26020031</a>}, number={231},
    journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel
    Bastian and Peitz, Sebastian}, year={2021} }'
  chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
    Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical
    and Computational Applications</i> 26, no. 2 (2021). <a href="https://doi.org/10.3390/mca26020031">https://doi.org/10.3390/mca26020031</a>.
  ieee: M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region
    Descent Method Using Radial  Basis Function Surrogate Models,” <i>Mathematical
    and Computational Applications</i>, vol. 26, no. 2, 2021.
  mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
    Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical
    and Computational Applications</i>, vol. 26, no. 2, 31, 2021, doi:<a href="https://doi.org/10.3390/mca26020031">10.3390/mca26020031</a>.
  short: M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26
    (2021).
date_created: 2021-03-01T10:46:48Z
date_updated: 2022-01-06T06:54:55Z
department:
- _id: '101'
- _id: '655'
doi: 10.3390/mca26020031
intvolume: '        26'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.mdpi.com/2297-8747/26/2/31/pdf
oa: '1'
publication: Mathematical and Computational Applications
publication_identifier:
  eissn:
  - 2297-8747
publication_status: published
status: public
title: Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis
  Function Surrogate Models
type: journal_article
user_id: '47427'
volume: 26
year: '2021'
...