Eduardo Casas
University of Cantabria
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Featured researches published by Eduardo Casas.
Computational Optimization and Applications | 2002
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
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
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
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
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
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
Eduardo Casas; Fredi Tröltzsch; Andreas Unger
{\mathbb R}^2
Siam Journal on Control and Optimization | 2001
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
Eduardo Casas; Juan Carlos De Los Reyes; Fredi Tröltzsch
O(h^{1 - 1/p})
Siam Journal on Control and Optimization | 1995
J. Frédéric Bonnans; Eduardo Casas
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