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From convergence principles to stability and optimality conditions


Klatte, Diethard; Kruger, Alexander; Kummer, Bernd (2012). From convergence principles to stability and optimality conditions. Journal of Convex Anaylsis, 19(4):1043-1072.

Abstract

We show in a rather general setting that Hoelder and Lipschitz stability properties ofsolutions 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 bothclassical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior ofsolution procedures.

Abstract

We show in a rather general setting that Hoelder and Lipschitz stability properties ofsolutions 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 bothclassical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior ofsolution procedures.

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6 citations in Web of Science®
7 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2012
Deposited On:11 Dec 2012 16:22
Last Modified:07 Sep 2017 08:41
Publisher:Heldermann Verlag
Series Name:Journal of Convex Analysis
ISSN:0944-6532
Other Identification Number:merlin-id:7703

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