An elliptic optimal control problem and its two relaxations

Emamizadeh, Behrouz and Farjudian, Amin and Mikayelyan, Hayk (2017) An elliptic optimal control problem and its two relaxations. Journal of Optimization Theory and Applications, 172 (2). pp. 455-465. ISSN 1573-2878

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Abstract

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.

Item Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10957-016-0983-1.
Keywords: Minimization; Free boundary; Optimality condition; Non-smooth analysis
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s10957-016-0983-1
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Depositing User: Yu, Tiffany
Date Deposited: 04 Mar 2019 10:33
Last Modified: 04 Mar 2019 10:33
URI: http://eprints.nottingham.ac.uk/id/eprint/56207

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