Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise Constraints

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• 作者：B. T. Kien ; V. H. Nhu ; N. H. Son
• 关键词：Second ; order necessary optimality condition ; Second ; order sufficient optimality condition ; Optimal control ; Semilinear elliptic equation ; Mixed pointwise constraint ; Strongly extended polyhedricity condition
• 刊名：Set-Valued and Variational Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：25
• 期：1
• 页码：177-210
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Probability Theory and Stochastic Processes;
• 出版者：Springer Netherlands
• ISSN：1877-0541
• 卷排序：25

文摘

This paper studies second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. We show that in some cases, there is a common critical cone under which the second-order necessary and sufficient optimality conditions for the problem are valid. Our results approach to a theory of no-gap second-order conditions. In order to obtain such results, we reduce the problem to a special mathematical programming problem with polyhedricity constraint set. We then use some tools of variational analysis and techniques of semilinear elliptic equations to analyze second-order conditions.