Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers

REGULARITY OF LAGRANGE MULTIPLIERS FOR OPTIMAL CONTROL PROBLEMS WITH PDEs AND MIXED CONTROL STATE CONSTRAINTS

Lagrange multipliers for distributed parameter systems with mixed control-state constraints may exhibit better regularity properties than those for problems with pure pointwise state constraints, (1), (2), (4). Under natural assumptions, they are functions of certain L-spaces, while Lagrange multpliers for pointwise state constraints are, in general, measures. Following an approach suggested in...

On the structure of Lagrange multipliers for state-constrained optimal control problems

Existence of Regular Lagrange Multipliers for a Nonlinear Elliptic Optimal Control Problem with Pointwise Control-State Constraints

A class of optimal control problems for semilinear elliptic equations with mixed control-state constraints is considered. The existence of bounded and measurable Lagrange multipliers is proven. As a particular application, the Lavrentiev type regularization of pointwise state constraints is discussed. Here, the existence of associated regular multipliers is shown, too.

Optimal Control of Problems Governed by Obstacle

In this paper we investigate optimal control problems governed by variational inequalities. We give optimality conditions under classical assumptions using a dual regularized functional to interpret the Variational Inequality. 1. Introduction. In this paper we investigate optimal control problems governed by vari-ational inequalities of obstacle type. This problem has been widely studied during...

Optimal Control of Semilinear Elliptic Obstacle Problems