Regularization for state constrained optimal control problems by half spaces based decoupling

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• 作者：Baasansuren Jadamba^b ; ^{bxjsma@rit.edu} ; Akhtar A. Khan^b ; ^{aaksma@rit.edu} ; Miguel Sama^a ; ^{msama@ind.uned.es}
• 关键词：Optimal control ; State constraints ; Lagrange multipliers ; Constraint qualification ; Cone of positive functions ; Halfspaces ; Conical decoupling ; Optimality conditions ; Regularization
• 刊名：Systems and Control Letters
• 出版年：2012
• 期刊代码：171_01676911
• 类别：et
• 出版时间：June, 2012
• 卷：61
• 期：6
• 页码：707-713
• 文件大小：442 K

摘要

In this paper, we study an abstract constrained optimization problem which subsumes a common model for the optimal control of linear partial differential equations. Our emphasis is the case when the ordering cone for the optimization problem has an empty interior. To circumvent this difficulty, we propose a new regularization approach which is based on the decoupling of the ordering cone by using certain half-spaces. The approach results in a family of regular optimization problems having a simpler structure than the original optimization problem. Existence theorems, convergence analysis, and optimality conditions are given for the regularized problems. We present two numerical examples and the results are quite encouraging, showing the potential of the proposed approach.