---
_id: '8752'
abstract:
- lang: eng
  text: In this article we develop a gradient-based algorithm for the solution of
    multiobjective optimization problems with uncertainties. To this end, an additional
    condition is derived for the descent direction in order to account for inaccuracies
    in the gradients and then incorporated into a subdivision algorithm for the computation
    of global solutions to multiobjective optimization problems. Convergence to a
    superset of the Pareto set is proved and an upper bound for the maximal distance
    to the set of substationary points is given. Besides the applicability to problems
    with uncertainties, the algorithm is developed with the intention to use it in
    combination with model order reduction techniques in order to efficiently solve
    PDE-constrained multiobjective optimization problems.
author:
- 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: 'Peitz S, Dellnitz M. Gradient-Based Multiobjective Optimization with Uncertainties.
    In: <i>NEO 2016</i>. Cham; 2017:159-182. doi:<a href="https://doi.org/10.1007/978-3-319-64063-1_7">10.1007/978-3-319-64063-1_7</a>'
  apa: Peitz, S., &#38; Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization
    with Uncertainties. In <i>NEO 2016</i> (pp. 159–182). Cham. <a href="https://doi.org/10.1007/978-3-319-64063-1_7">https://doi.org/10.1007/978-3-319-64063-1_7</a>
  bibtex: '@inproceedings{Peitz_Dellnitz_2017, place={Cham}, title={Gradient-Based
    Multiobjective Optimization with Uncertainties}, DOI={<a href="https://doi.org/10.1007/978-3-319-64063-1_7">10.1007/978-3-319-64063-1_7</a>},
    booktitle={NEO 2016}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2017},
    pages={159–182} }'
  chicago: Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective
    Optimization with Uncertainties.” In <i>NEO 2016</i>, 159–82. Cham, 2017. <a href="https://doi.org/10.1007/978-3-319-64063-1_7">https://doi.org/10.1007/978-3-319-64063-1_7</a>.
  ieee: S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with
    Uncertainties,” in <i>NEO 2016</i>, 2017, pp. 159–182.
  mla: Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization
    with Uncertainties.” <i>NEO 2016</i>, 2017, pp. 159–82, doi:<a href="https://doi.org/10.1007/978-3-319-64063-1_7">10.1007/978-3-319-64063-1_7</a>.
  short: 'S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182.'
date_created: 2019-03-29T13:28:56Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1007/978-3-319-64063-1_7
language:
- iso: eng
page: 159-182
place: Cham
project:
- _id: '52'
  name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: NEO 2016
publication_identifier:
  isbn:
  - '9783319640624'
  - '9783319640631'
  issn:
  - 1860-949X
  - 1860-9503
publication_status: published
status: public
title: Gradient-Based Multiobjective Optimization with Uncertainties
type: conference
user_id: '47427'
year: '2017'
...