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Sufficient second-order optimality conditions for an elliptic optimal control problem with pointwise control-state constraints. (English) Zbl 1119.49022

Summary: An optimal control problem for a semilinear elliptic equation is investigated, where pointwise constraints are given on control and state. The state constraints are of mixed (bottleneck) type, where associated Lagrange multipliers can be chosen as bounded and measurable functions. Based on this property, a second-order sufficient optimality condition is established that takes into account strongly active constraints.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
90C48 Programming in abstract spaces
35J25 Boundary value problems for second-order elliptic equations
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