The Optimal Control Problems for Generalized Elliptic Quasivariational Inequalities

Abstract

In this article, we propose an optimal control problem for generalized elliptic quasi-variational inequality with unilateral constraints. Then, we discuss the sufficient assumptions that ensure the convergence of the solutions to the optimal control problem. The proofs depend on convergence results for generalized elliptic quasi-variational inequalities, obtained by the arguments of compactness, lower semi-continuity, monotonicity, penalty and different estimates. As an application, we addressed the abstract convergence results in the analysis of optimal control associated with boundary value problems.

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“…It is well documented that the study of variational inequality, which was initiated by Stampacchia [1] becomes a very productive and fruitful tool to examine several problems arising in the natural sciences. Due to an application oriented nature, this field of research has been expanded and generalized in several directions, see [2][3][4][5][6][7][8]. One of the pronounced generalizations of variational inequality is quasi-variational inequality (QVI) which is to find p * ∈ K(p * ), such that:…”

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