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An Elliptic Optimal Control Problem and its Two Relaxations
The University of Nottingham Ningbo, Ningbo, China.
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).ORCID iD: 0000-0002-1879-0763
The University of Nottingham Ningbo, Ningbo, China.
2017 (English)In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 172, no 2, 455-465 p.Article in journal (Refereed) Published
Abstract [en]

In this note, we consider a control theory problem involving a strictly convex energy functional, which is not Gâteaux differentiable. The functional came up in the study of a shape optimization problem, and here we focus on the minimization of this functional. We relax the problem in two different ways and show that the relaxed variants can be solved by applying some recent results on two-phase obstacle-like problems of free boundary type. We derive an important qualitative property of the solutions, i.e., we prove that the minimizers are three-valued, a result which significantly reduces the search space for the relevant numerical algorithms. © 2016, Springer Science+Business Media New York.

Place, publisher, year, edition, pages
New York, NY: Springer, 2017. Vol. 172, no 2, 455-465 p.
Keyword [en]
Minimization, Free boundary, Optimality condition, Non-smooth analysis
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-32086DOI: 10.1007/s10957-016-0983-1ISI: 000394266600006Scopus ID: 2-s2.0-84978701718OAI: oai:DiVA.org:hh-32086DiVA: diva2:974703
Available from: 2016-09-27 Created: 2016-09-27 Last updated: 2017-11-29Bibliographically approved

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Farjudian, Amin

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