Geodesic
Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 581-600

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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.

DOI : 10.1051/cocv/2009010
Classification : 49J20, 49K20, 35J65
Keywords: optimal control, pointwise state constraints, first and second order optimality conditions, Lagrange multipliers, Borel measures 
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     author = {Casas, Eduardo and Tr\"oltzsch, Fredi},
     title = {Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {581--600},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {3},
     year = {2010},
     doi = {10.1051/cocv/2009010},
     mrnumber = {2674627},
     zbl = {1201.49004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009010/}
}
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Casas, Eduardo; Tröltzsch, Fredi. Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 581-600. doi: 10.1051/cocv/2009010

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