This paper deals with the optimal control of an obstacle problem where the control variable is the obstacle. The state system is described by a class of quasilinear elliptic variational inequalitie...

Optimal Obstacle Control Problems Involving Nonsmooth Cost Functionals and Quasilinear Variational Inequalities

In this paper, some existence results for optimal control problems governed by abstract quasi-variational inequalities are proved in reflexive Banach spaces. As an application, an existence of the optimal control for the bilateral obstacle optimal control problem is also given under some suitable conditions, in which the state satisfies a quasilinear elliptic variational inequality with a source term.

https://projecteuclid.org/download/pdf_1/euclid.twjm/1500406733

The existence results for optimal control problems governed by quasi-variational inequalities in reflexive banach spaces

A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the existence and uniqueness of the optimal control and its associated state system. The objective of this work is to make the numerical analysis of the above optimal control problem, through the finite element method with Lagrange's triangles of type 1. We discretize the elliptic variational inequality which define the state system and the corresponding cost functional, and we prove that there exists a discrete optimal control and its associated discrete state system for each positive $h$ (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter $h$ goes to zero.

Numerical analysis of distributed optimal control problems governed by elliptic variational inequalities

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality with a source term and the control functions are the upper and the lower obstacles. We assume that the obstacles φ and ψ are in W 2 , 2 ( Ω ) , but this causes difficulty for deriving the optimality condition. By applying the weak convergence method, we establish existence and incomplete necessary conditions for the optimal control.

Bilateral obstacle optimal control for a quasilinear elliptic variational inequality with a source term

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Bilateral obstacle optimal control for a quasilinear elliptic variational inequality with a source term