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Aubin Property and Uniqueness of Solutions in Cone Constrained Optimization

Diethard Klatte (diethard.klatte***at***business.uzh.ch)
Bernd Kummer (kummer***at***mathematik.hu-berlin.de)

Abstract: We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in \cite{KlaKum02}. 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.

Keywords: Cone constrained optimization, Aubin property, critical points, constraint nondegeneracy, locally single-valued solutions

Category 1: Nonlinear Optimization

Category 2: Complementarity and Variational Inequalities

Category 3: Convex and Nonsmooth Optimization

Citation: Preprint, University of Zurich, June 2012 Final version published in: Mathematical Methods of Operations Research (2013) 77(3): 291-304

Download: [PDF]

Entry Submitted: 07/06/2012
Entry Accepted: 07/06/2012
Entry Last Modified: 02/24/2016

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