---
_id: '8750'
abstract:
- lang: eng
  text: In this article we propose a descent method for equality and inequality constrained
    multiobjective optimization problems (MOPs) which generalizes the steepest descent
    method for unconstrained MOPs by Fliege and Svaiter to constrained problems by
    using two active set strategies. Under some regularity assumptions on the problem,
    we show that accumulation points of our descent method satisfy a necessary condition
    for local Pareto optimality. Finally, we show the typical behavior of our method
    in a numerical example.
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: 'Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality
    Constrained Multiobjective Optimization Problems. In: <i>Numerical and Evolutionary
    Optimization – NEO 2017</i>. Cham; 2018. doi:<a href="https://doi.org/10.1007/978-3-319-96104-0_2">10.1007/978-3-319-96104-0_2</a>'
  apa: Gebken, B., Peitz, S., &#38; Dellnitz, M. (2018). A Descent Method for Equality
    and Inequality Constrained Multiobjective Optimization Problems. In <i>Numerical
    and Evolutionary Optimization – NEO 2017</i>. Cham. <a href="https://doi.org/10.1007/978-3-319-96104-0_2">https://doi.org/10.1007/978-3-319-96104-0_2</a>
  bibtex: '@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent
    Method for Equality and Inequality Constrained Multiobjective Optimization Problems},
    DOI={<a href="https://doi.org/10.1007/978-3-319-96104-0_2">10.1007/978-3-319-96104-0_2</a>},
    booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken,
    Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }'
  chicago: Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method
    for Equality and Inequality Constrained Multiobjective Optimization Problems.”
    In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham, 2018. <a href="https://doi.org/10.1007/978-3-319-96104-0_2">https://doi.org/10.1007/978-3-319-96104-0_2</a>.
  ieee: B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality
    Constrained Multiobjective Optimization Problems,” in <i>Numerical and Evolutionary
    Optimization – NEO 2017</i>, 2018.
  mla: Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained
    Multiobjective Optimization Problems.” <i>Numerical and Evolutionary Optimization
    – NEO 2017</i>, 2018, doi:<a href="https://doi.org/10.1007/978-3-319-96104-0_2">10.1007/978-3-319-96104-0_2</a>.
  short: 'B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization
    – NEO 2017, Cham, 2018.'
conference:
  name: 'NEO 2017: Numerical and Evolutionary Optimization'
date_created: 2019-03-29T13:26:47Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1007/978-3-319-96104-0_2
language:
- iso: eng
place: Cham
publication: Numerical and Evolutionary Optimization – NEO 2017
publication_identifier:
  isbn:
  - '9783319961033'
  - '9783319961040'
  issn:
  - 1860-949X
  - 1860-9503
publication_status: published
status: public
title: A Descent Method for Equality and Inequality Constrained Multiobjective Optimization
  Problems
type: conference
user_id: '47427'
year: '2018'
...