Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems

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• 作者：Eduardo Casas ; Fredi Tröltzsch
• 关键词：Optimal control ; Parabolic equation ; Semilinear equation ; Second ; order optimality conditions ; Weak local minimum ; Strong local minimum
• 刊名：Vietnam Journal of Mathematics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：44
• 期：1
• 页码：181-202
• 全文大小：398 KB
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• 作者单位：Eduardo Casas (1)
  Fredi Tröltzsch (2)
  
  1. Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005, Santander, Spain
  2. Institut für Mathematik, Technische Universität Berlin, 10623, Berlin, Germany
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2305-2228

文摘

Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regularization term. Here, standard second-order conditions cannot be expected to hold. For this case, new second-order conditions are established that are based on different types of critical cones. Depending on the choice of this cones, the second-order conditions are sufficient for local minima that are weak or strong in the sense of calculus of variations.