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Full stability of locally optimal solutions in second-order cone programming

Boris Mordukhovich (boris***at***math.wayne.edu)
Jiri Outrata (outrata***at***utia.cas.cz)
Ebrahim Sarabi (ebrahim.sarabi***at***math.wayne.edu)

Abstract: The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to problems of second-order cone programming (SOCP) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sucient conditions under the corresponding constraint quali cations. We also establish close relationships between full stability of local minimizers for SOCPs and strong regularity of the associated generalized equations at nondegenerate points. Our approach is mainly based on advanced tools of second-order variational analysis and generalized di erentiation.

Keywords: variational analysis, second-order cone programming, full stability of local minimizers, nondegeneracy, strong regularity, quadratic growth, second-order subdi

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 07/12/2013
Entry Accepted: 07/13/2013
Entry Last Modified: 07/13/2013

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