Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Issue		ESAIM: COCV Volume 16, Number 3, July-September 2010


Page(s)		581 - 600
DOI		10.1051/cocv/2009010
Published online		02 July 2009

ESAIM: COCV 16 (2010) 581-600

Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas¹ and Fredi Tröltzsch²

¹ Dpt. Matemática Aplicada y Ciencias de la Computación, E.T.S.I.I. y T., Universidad de Cantabria, Av. Los Castros s/n, 39005 Santander, Spain. eduardo.casas@unican.es
² Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany. troeltzsch@math.tu-berlin.de

Received: 20 July 2008
Revised: 24 February 2009

Abstract

Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.

Mathematics Subject Classification: 49J20 / 49K20 / 35J65.

Key words: Optimal control / pointwise state constraints / first and second order optimality conditions / Lagrange multipliers / Borel measures.

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