generalized equations Hoelder stability iteration schemes calmness Aubin property variational principles From convergence principles to stability and optimality Diethard Klatte Klatte Diethard Alexander Kruger Kruger Alexander Bernd Kummer Kummer Bernd Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 19, 22 Seiten

From convergence principles to stability and optimality

Diethard Klatte , Alexander Kruger , Bernd Kummer

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 19, 22 Seiten

MSC 2000

49J53 Set-valued and variational analysis
49K40 Sensitivity, stability, well-posedness

Abstract
We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be derived. Our most abstract models are (multi-) functions on complete metric spaces. The relevance of this approach is illustrated by deriving both classical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior of solution procedures.

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