Maïtine Bergounioux

Primal-Dual Strategy for Constrained Optimal Control Problems

An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of the strict complementarity condition is discussed.

A Comparison of a Moreau--Yosida-Based Active Set Strategy and Interior Point Methods for Constrained Optimal Control Problems

This research is devoted to the numerical solution of constrained optimal control problems governed by elliptic partial differential equations. The main purpose is a comparison between a recently developed Moreau--Yosida-based active set strategy involving primal and dual variables and two implementations of interior point algorithms.

Primal-Dual Strategy for State-Constrained Optimal Control Problems

State constrained optimal control problems represent severe analytical and numerical challenges. A numerical algorithm based on an active set strategy involving primal as well as dual variables, suggested by a generalized Moreau-Yosida regularization of the state constraint is proposed and analyzed. Numerical examples are included.

Augemented Lagrangian Techniques for Elliptic State Constrained Optimal Control Problems

We propose augmented Lagrangian methods to solve state and control constrained optimal control problems. The approach is based on the Lagrangian formulation of nonsmooth convex optimization in Hilbert spaces developed in [K. Ito and K. Kunisch, Augmented Lagrangian Methods for Nonsmooth Convex Optimization in Hilbert Spaces, preprint, 1994]. We investigate a linear optimal control problem with a boundary control function as in [M. Bergounioux, Numer. Funct. Anal. Optim., 14 (1993), pp. 515--543]. Both the equation and the constraints are augmented. The proposed methods are general and can be adapted to a much wider class of problems.

Optimal control of an obstacle problem

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.

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.

General Optimality Conditions for Constrained Convex Control Problems

In this paper we investigate some optimal convex control problems, with mixed constraints on the state and the control. We give a general condition which allows us to set optimality conditions for nonqualified problems (in the Slater sense). Then we give some applications and examples involving generalized bang-bang results.

A penalization method for optimal control of elliptic problems with state constraints

In this paper boundary or distributed stationary control problems are studied in relation to an elliptic operator and state and control constraints. Different kinds of conditions are formulated to prove the existence of a decoupled optimality system and Lagrange multipliers.

Augmented Lagrangian method for distributed optimal control problems with state constraints

We consider state-constrained optimal control problems governed by elliptic equations. Doing Slater-like assumptions, we know that Lagrange multipliers exist for such problems, and we propose a decoupled augmented Lagrangian method. We present the algorithm with a simple example of a distributed control problem.

Optimal Control of Bilateral Obstacle Problems

We consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H2 norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case is studied that needs no compactness assumption, via a monotonicity method.