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Aubin property and uniqueness of solutions in cone constrained optimization

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  • Diethard Klatte
  • Bernd Kummer

Abstract

We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in Klatte and Kummer (Nonsmooth equations in optimization. Kluwer, Dordrecht, 2002 ). In particular, we show that constraint nondegeneracy and hence uniqueness of the multiplier is necessary for the Aubin property of the critical point map. Moreover, we give conditions under which the critical point map has the Aubin property if and only if it is locally single-valued and Lipschitz. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Diethard Klatte & Bernd Kummer, 2013. "Aubin property and uniqueness of solutions in cone constrained optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 291-304, June.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:3:p:291-304
    DOI: 10.1007/s00186-013-0429-6
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    2. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
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