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M.Bergounioux; F.Tröltzsch : Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type

M.Bergounioux; F.Tröltzsch : Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type

Author(s) :
M.Bergounioux; F.Tröltzsch
Title :
Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-19, 1998
Mathematics Subject Classification :
49K20 [ Optimal control problems with PDE (nec./ suff.) ]
90C48 [ Programming in abstract spaces ]
90C45 [ Continuous programming ]
Abstract :
We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear programming problems.
Keywords :
parabolic equation, optimal control, pointwise state-constraint, bottleneck problem
Language :
english
Publication time :
10/1998