An elliptic optimal control problem and its two relaxations
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/56207/ |
| _version_ | 1848799293145612288 |
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| author | Emamizadeh, Behrouz Farjudian, Amin Mikayelyan, Hayk |
| author_facet | Emamizadeh, Behrouz Farjudian, Amin Mikayelyan, Hayk |
| author_sort | Emamizadeh, Behrouz |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:33:22Z |
| format | Article |
| id | nottingham-56207 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:33:22Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-562072019-03-04T10:33:15Z https://eprints.nottingham.ac.uk/56207/ An elliptic optimal control problem and its two relaxations Emamizadeh, Behrouz Farjudian, Amin Mikayelyan, Hayk 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. Springer 2017-02-28 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/56207/1/2017-Emamizadeh_Farjudian_Mikayelyan-Elliptic_Optimal_Control_Problem.pdf Emamizadeh, Behrouz, 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 Minimization; Free boundary; Optimality condition; Non-smooth analysis https://link.springer.com/article/10.1007%2Fs10957-016-0983-1 doi:10.1007/s10957-016-0983-1 doi:10.1007/s10957-016-0983-1 |
| spellingShingle | Minimization; Free boundary; Optimality condition; Non-smooth analysis Emamizadeh, Behrouz Farjudian, Amin Mikayelyan, Hayk An elliptic optimal control problem and its two relaxations |
| title | An elliptic optimal control problem and its two relaxations |
| title_full | An elliptic optimal control problem and its two relaxations |
| title_fullStr | An elliptic optimal control problem and its two relaxations |
| title_full_unstemmed | An elliptic optimal control problem and its two relaxations |
| title_short | An elliptic optimal control problem and its two relaxations |
| title_sort | elliptic optimal control problem and its two relaxations |
| topic | Minimization; Free boundary; Optimality condition; Non-smooth analysis |
| url | https://eprints.nottingham.ac.uk/56207/ https://eprints.nottingham.ac.uk/56207/ https://eprints.nottingham.ac.uk/56207/ |