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.

Author information

Contact details are reproduced from the original publication and may be historical.

Diethard Klatte

Institut für Operations Research, Universität Zürich, Moussonstrasse 15, 8044 Zürich, Switzerland

klatte@ior.uzh.ch

Alexander Kruger

Centre for Informatics and Applied Optimization, University of Ballarat, POB 663, Ballarat, Vic. 3350, Australia

a.kruger@ballarat.edu.au

Bernd Kummer

Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany

kummer@math.hu-berlin.de

Keywords

  • Generalized equations
  • Hoelder stability
  • iteration schemes
  • calmness
  • Aubin property
  • variational principles

Mathematics Subject Classification

49J53, 49K40, 90C31, 65J05

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Suggested citation

D. Klatte, A. Kruger, B. Kummer. “From Convergence Principles to Stability and Optimality Conditions.” Journal of Convex Analysis 19 (2012), No. 4, 1043–1072. https://doi.org/10.68381/jca19056

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.