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## Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise state constraints

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Author(s) : Arnd Rösch , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 0733-2002

MSC 2000

49K20 Problems involving partial differential equations
90C48 Programming in abstract spaces

Abstract :
An optimal control problem for a semilinear parabolic equation is investigated, where pointwise constraints are given on the control and the state. The state constraints are of mixed (bottleneck) type, where associated Lagrange multipliers can assumed to be bounded and measurable functions. Based on this property, a second-order sufficient optimality condition is established that considers strongly active constraints.

Keywords : Optimal control, heat equation, parabolic differential equation, sufficient second-order optimality condition,pointwise mixed control-state constraints, bottleneck constraints