Optimal control of variational inequalities.

Optimal control of variational inequalities by V. Barbu Download PDF EPUB FB2

Optimality systems for optimal control problems governed by elliptic variational inequalities are derived. Existence of appropriately defined Lagrange multipliers is proved. A primal—dual active set method is proposed to solve the optimality systems numerically. Examples with and without lack of strict complementarity are by: Optimal control of variational inequalities.

Boston: Pitman Advanced Pub. Program, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Viorel Barbu. In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle.

The main tools used are the Ekeland's variational principle combined with penalization and spike variation by: select article Chapter 3 Optimal Stopping-Time Problems and Variational Inequalities. Recently, optimal control problems for variational–hemivariational inequalities have been studied in where existence of optimal pairs is proved and necessary optimality conditions of first order are derived, and in, where existence of optimal pairs Author: Danfu Han, Weimin Han, Stanisław Migórski, Stanisław Migórski, Junfeng Zhao.

Optimal control problems for variational and hemivariational inequalities have been discussed in several works, including,. Due to the nonsmooth and nonconvex feature of the functionals involved, the treatment of optimal control problems for such inequalities requires the use of their approximation by smooth optimization by: Abstract.

We investigate optimal control problems governed by variational inequalities. and more precisely the obstacle problem. Since we adopt a numerical point of view, we first relax the feasible domain of the problem; then using both mathematical programming methods and penalization methods we get optimality conditions with smooth Lagrange multipliers.

Abstract. This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff.

We study a special case of an optimal control problem governed by a differential equation and a differential rate--independent variational inequality, both with given initial conditions.

Under certain conditions, the variational inequality can be reformulated as a differential inclusion with discontinuous right-hand side.

This inclusion is known as sweeping process. With viscous incompressible fluid flows as application background, stability is analyzed for solutions with respect to perturbations in the superpotential and the density of external forces.

We also present a result on the existence of a solution to an optimal control problem for the stationary Stokes hemivariational inequality.

Optimal control of variational inequalities: A mathematical programming approach. Modelling and Optimization of Distributed Parameter Systems Applications to engineering, () Optimality conditions for strongly monotone variational inequalities.

Abstract. In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is comple-mented with pointwise control constraints. The convergence of a smoothing scheme is analyzed.

There, the variational inequality is replaced by a semilinear elliptic equation. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality.

The present paper represents a continuationa continuous dependence result for the solution of an elliptic variational–hemivariational inequality was obtained and then used to prove the existence of optimal pairs for two associated optimal control problems.

Variational Inequality Optimal Control Problem Complementarity Problem Variational Inequality Problem Level Problem These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Variational Inequality Optimal Control Problem Variational Equation Penalty Method Discrete Problem These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

() Strong Stationarity for Optimal Control of a Nonsmooth Coupled System: Application to a Viscous Evolutionary Variational Inequality Coupled with an Elliptic PDE. SIAM Journal on Optimization Necessary Optimality Conditions for Control of Strongly Monotone Variational Inequalities.

Control of Distributed Parameter and Stochastic Systems, () On Optimization Problems with Variational Inequality Constraints. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems.

The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. We study the optimal control of systems governed by variational inequalities.

We transform the problem into a linear problem with constraints on the state. With this formulation, the existence of necessary optimality conditions is proven for a large class of.

One of the most successful and numerically efficient techniques to obtain the optimality system for the optimal control problem for variational inequalities is the so called primal-dual active set.() Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality.

International Journal of Differential Equations() Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints.In this paper, we consider the numerical solution of optimal control problems for variational–hemivariational inequalities or hemivariational inequalities, and prove the convergence of numerical solutions under rather general assumptions.