Full Stability of Locally Optimal Solutions in Second-Order Cone Programs

The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-o...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 24; no. 4; pp. 1581 - 1613
Main Authors: Mordukhovich, Boris S., Outrata, Jiří V., Sarabi, M. Ebrahim
Format: Journal Article
Language:English
Published: 01.01.2014
Subjects:
Differentiation
Mathematical analysis
Optimization
Regularity
Stability
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sufficient conditions under the corresponding constraint qualifications. 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 differentiation.
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ISSN:1052-6234
1095-7189
DOI:10.1137/130928637