Sufficient Second‐Order Optimality Conditions for an Elliptic Optimal Control Problem with Pointwise Control‐State Constraints | Zendy

Arnd Rösch | Zendy; Fredi Tröltzsch | Zendy

Open Access

Sufficient Second‐Order Optimality Conditions for an Elliptic Optimal Control Problem with Pointwise Control‐State Constraints

Author(s) -

Arnd Rösch,

Fredi Tröltzsch

Publication year - 2006

Publication title -

siam journal on optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.066

H-Index - 136

eISSN - 1095-7189

pISSN - 1052-6234

DOI - 10.1137/050625850

Subject(s) - pointwise , mathematics , lagrange multiplier , optimal control , bounded function , state (computer science) , bottleneck , order (exchange) , mathematical optimization , control (management) , mathematical analysis , computer science , finance , algorithm , artificial intelligence , economics , embedded system

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 be assumed to be bounded and measurable functions. Based on this property, a second-order sufficient optimality condition is established that considers strongly active constraints.

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