Eduardo Casas

Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem

We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.

Control of an elliptic problem with pointwise state constraints

This paper deals with a quadratic control problem for elliptic equations with pointwise state constraints. Existence and uniqueness of the solution is proved. Optimality conditions are given and regularity of the optimal solution is investigated.

Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations

This paper deals with state-constrained optimal control problems governed by semilinear parabolic equations. We establish a minimum principle of Pontryagins type. To deal with the state constraints, we introduce a penalty problem by using Ekelands principle. The key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined. Conditions for normality of optimality conditions are given.

Boundary control of semilinear elliptic equations with pointwise state constraints

This paper is concerned with state constrained optimal control problems of semilinear elliptic equations, the control being on the boundary. Optimality conditions are derived and regularity of the optimal solution is investigated.

Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking piecewise constant controls. Finally, error estimates are established and some numerical experiments, which confirm the theoretical results, are performed.

Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in

Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations

{\mathbb R}^2

Second Order Optimality Conditions for Semilinear Elliptic Control Problems with Finitely Many State Constraints

. Piecewise linear finite elements are used to approximate the control as well as the state. We prove that the error estimates are of order

Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints

O(h^{1 - 1/p})

An Extension of Pontryagin's Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities

for some