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Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino;  Ira Neitzel;  Fredi Tröltzsch — 2010

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino;  Fredi Tröltzsch;  Boris Vexler — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.

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