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Dive into the research topics where Eduardo Casas is active.

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Featured researches published by Eduardo Casas.


Computational Optimization and Applications | 2002

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

Nadir Arada; Eduardo Casas; Fredi Tröltzsch

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.


Siam Journal on Control and Optimization | 1986

Control of an elliptic problem with pointwise state constraints

Eduardo Casas

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.


Siam Journal on Control and Optimization | 1997

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

Eduardo Casas

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.


Siam Journal on Control and Optimization | 1993

Boundary control of semilinear elliptic equations with pointwise state constraints

Eduardo Casas

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.


Computational Optimization and Applications | 2005

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

Eduardo Casas; Mariano Mateos; Fredi Tröltzsch

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.


Siam Journal on Control and Optimization | 2006

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

Eduardo Casas; Jean-Pierre Raymond

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


Siam Journal on Control and Optimization | 2000

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

Eduardo Casas; Fredi Tröltzsch; Andreas Unger

{\mathbb R}^2


Siam Journal on Control and Optimization | 2001

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

Eduardo Casas; Mariano Mateos

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


Siam Journal on Optimization | 2008

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

Eduardo Casas; Juan Carlos De Los Reyes; Fredi Tröltzsch

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


Siam Journal on Control and Optimization | 1995

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

J. Frédéric Bonnans; Eduardo Casas

for some

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Fredi Tröltzsch

Technical University of Berlin

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Karl Kunisch

Austrian Academy of Sciences

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Gerd Wachsmuth

Chemnitz University of Technology

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Jean-Pierre Raymond

Institut de Mathématiques de Toulouse

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Konstantinos Chrysafinos

National Technical University of Athens

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Andreas Unger

Chemnitz University of Technology

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Roland Herzog

Chemnitz University of Technology

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Christopher Ryll

Technical University of Berlin

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