Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities

Convergence of distributed optimal control problems governed by elliptic variational inequalities

First, let ug be the unique solution of an elliptic variational inequality with source term g. We establish, in the general case, the error estimate between u3(μ) = μug1 + (1 − μ)ug2 and u4(μ) = uμg1+(1−μ)g2 for μ ∈ [0, 1]. Secondly, we consider a family of distributed optimal control problems governed by elliptic variational inequalities over the internal energy g for each positive heat transf...

Optimal Control of Problems Governed by Abstract Elliptic Variational Inequalities with State Constraints∗

In this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints. We present a relaxed formulation for the problem. With penalization methods and approximation techniques we give qualification conditions to get first-order optimality conditions.

Existence Theorems for Nonconvex Variational Inequalities Problems

In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...

Necessary Optimality Conditions for Control of Strongly Monotone Variational Inequalities

In this paper we derive necessary optimality conditions involving Mordukhovich coderivatives for optimal control problems of strongly monotone variational inequalities.

A Fully Discrete Approximation for Control Problems Governed by Parabolic Variational Inequalities