An Elliptic Optimal Control Problem and its Two Relaxations

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• 作者：Behrouz Emamizadeh ; Amin Farjudian…
• 关键词：Minimization ; Free boundary ; Optimality condition ; Non ; smooth analysis
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：172
• 期：2
• 页码：455-465
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

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.