Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control Problems | Zendy

Roland Griesse | Zendy

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Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control Problems

Author(s) -

Roland Griesse

Publication year - 2006

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1300

Subject(s) - lipschitz continuity , stability (learning theory) , state (computer science) , mathematics , optimal control , control theory (sociology) , control (management) , mathematical optimization , computer science , mathematical analysis , algorithm , machine learning , artificial intelligence

In this paper, optimal control problems with pointwise state constraints for linear and semilinear elliptic partial differential equations are studied. The problems are subject to perturbations in the problem data. Lipschitz stability with respect to perturbations of the optimal control and the state and adjoint variables is established initially for linear–quadratic problems. Both the distributed and Neumann boundary control cases are treated. Based on these results, and using an implicit function theorem for generalized equations, Lipschitz stability is also shown for an optimal control problem involving a semilinear elliptic equation.

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