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Local minimizers of functionals with multiple volume constraints


Oudet, Édouard; Rieger, Marc Oliver (2008). Local minimizers of functionals with multiple volume constraints. ESAIM: Control, Optimisation and Calculus of Variations, 14(4):780-794.

Abstract

We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a $\Gamma$-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.

Abstract

We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a $\Gamma$-limit argument and illustrate this with numerical computations. Finally we construct explicitly local and global minimizers for problems with two volume constraints.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Volume constrained problems, numerical simulations, level set method, local minima
Language:English
Date:7 February 2008
Deposited On:05 Dec 2008 09:52
Last Modified:20 Jun 2016 17:46
Publisher:EDP Sciences
ISSN:1262-3377
Publisher DOI:https://doi.org/10.1051/cocv:2008013
Official URL:http://www.esaim-cocv.org

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