---
res:
bibo_abstract:
- "Multiobjective optimization plays an increasingly important role in modern\r\napplications,
where several objectives are often of equal importance. The task\r\nin multiobjective
optimization and multiobjective optimal control is therefore\r\nto compute the
set of optimal compromises (the Pareto set) between the\r\nconflicting objectives.
Since the Pareto set generally consists of an infinite\r\nnumber of solutions,
the computational effort can quickly become challenging\r\nwhich is particularly
problematic when the objectives are costly to evaluate as\r\nis the case for models
governed by partial differential equations (PDEs). To\r\ndecrease the numerical
effort to an affordable amount, surrogate models can be\r\nused to replace the
expensive PDE evaluations. Existing multiobjective\r\noptimization methods using
model reduction are limited either to low parameter\r\ndimensions or to few (ideally
two) objectives. In this article, we present a\r\ncombination of the reduced basis
model reduction method with a continuation\r\napproach using inexact gradients.
The resulting approach can handle an\r\narbitrary number of objectives while yielding
a significant reduction in\r\ncomputing time.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Banholzer, Stefan
foaf_surname: Banholzer
- foaf_Person:
foaf_givenName: Bennet
foaf_name: Gebken, Bennet
foaf_surname: Gebken
foaf_workInfoHomepage: http://www.librecat.org/personId=32643
- foaf_Person:
foaf_givenName: Michael
foaf_name: Dellnitz, Michael
foaf_surname: Dellnitz
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: https://orcid.org/0000-0002-3389-793X
- foaf_Person:
foaf_givenName: Stefan
foaf_name: Volkwein, Stefan
foaf_surname: Volkwein
bibo_doi: 10.1007/978-3-030-79393-7_3
dct_date: 2022^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/978-3-030-79392-0
dct_language: eng
dct_publisher: Springer@
dct_title: ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical
Continuation@
...