Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems
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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.
KeywordsOptimal control Parabolic equation Semilinear equation Second-order optimality conditions Weak local minimum Strong local minimum
Mathematics Subject Classification (2010)49J20 49K20
The first author was partially supported by Spanish Ministerio de Economía y Competitividad under projects MTM2011-22711 and MTM2014-57531-P. The second is supported by DFG in the framework of the Collaborative Research Center SFB 910, project B6.
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