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Optimal control problems for quasi-variational inequalities and its numerical approximation

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  • The main objective of this paper is to discuss about optimal control problems in which the state equations may have multiple solutions. Our state equations are represented by the so-called quasi-variational inequalities and some difficulties for the mathematical treatment arise from such a structure. From the numerical point of view we propose a class of regular approximations for them in which state equations are uniquely solved and the control spaces are relaxed, and further a class of their time-discretizations which are schemes of usual elliptic optimal control problems.
    Mathematics Subject Classification: Primary: 35K45; Secondary: 35K50.


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