Set-Valued and Variational Analysis

, Volume 25, Issue 1, pp 177–210 | Cite as

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

  • B. T. KienEmail author
  • V. H. Nhu
  • N. H. Son


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.


Second-order necessary optimality condition Second-order sufficient optimality condition Optimal control Semilinear elliptic equation Mixed pointwise constraint Strongly extended polyhedricity condition 

Mathematics Subject Classification (2010)

49K20 35J25 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Optimization and Control TheoryInstitute of Mathematics, Vietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHanoiVietnam
  3. 3.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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