Aubin property and uniqueness of solutions in cone constrained optimization

Diethard Klatte () and Bernd Kummer ()

Mathematical Methods of Operations Research, 2013, vol. 77, issue 3, 304 pages

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

Keywords: Cone constrained optimization; Aubin property; Critical points; Constraint nondegeneracy; Locally single-valued solutions; 49K40; 90C31; 49J53; 90C22 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00186-013-0429-6

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