The existence results for obstacle optimal control problems

Yuquan Ye, Chi Kin Chan, Heung Wing Joseph Lee

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


This paper is concerned with the existence of an optimal control problem for a quasi-linear elliptic obstacle variational inequality in which the obstacle is taken as the control. Firstly, we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in Section 2. In Section 3, as an application, without the assumption of the monotone type mapping for the leading operator of the variational inequality, we prove that the leading operator of the variational inequality is a monotone type mapping. Existence of the optimal obstacle is proved. The method used here is different from [Y.Y. Zhou, X.Q. Yang, K.L. Teo, The existence results for optimal control problems governed by a variational inequality, J. Math. Anal. Appl. 321 (2006) 595-608].
Original languageEnglish
Pages (from-to)451-456
Number of pages6
JournalApplied Mathematics and Computation
Issue number2
Publication statusPublished - 15 Aug 2009


  • Existence
  • Obstacle optimal control
  • Variational inequality

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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