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From convergence principles to stability and optimality conditions

Diethard Klatte(klatte***at***ior.unizh.ch)
Alexander Kruger(a.kruger***at***ballarat.edu.au)
Bernd Kummer(kummer***at***math.hu-berlin.de)

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.

Keywords: Generalized equations, Hoelder stability, iteration schemes, calmness, Aubin property, variational principles

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 12/02/2010
Entry Accepted: 12/07/2010
Entry Last Modified: 12/02/2010

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