Optimal Control Problem Governed By Elliptic Variational Inequalities For Infinite Order

S.A. El-Zahaby; Ibtissam Mohamed El-Zoulati

S.A. El-Zahaby Department of Mathematics, Faculty of Science, Al Azhar University(Girls) Nasr City, Cairo, Egypt
Ibtissam Mohamed El-Zoulati Department of Mathematics, Faculty of Science, Al Azhar University(Girls) Nasr City, Cairo, Egypt

Keywords: Control problem, variational inequalities, bilinear form, cost function, conical derivative.

Abstract

In this paper we find, the necessary conditions for optimality of a system governed by elliptic variational inequalities of infinite order with obstacle, where the cost function is quadratic associated with the state y (u). When there is no constraint on the control variable, we give the first order necessary conditions of the optimality systems.

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