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

Boris S. Mordukhovich; Jiri V. Outrata; M. Ebrahim Sarabi

doi:10.1137/130928637

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

Boris S. Mordukhovich, Jiri V. Outrata, M. Ebrahim Sarabi

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1581-1613
Number of pages	33
Journal	SIAM Journal on Optimization
Volume	24
Issue number	4
DOIs	https://doi.org/10.1137/130928637
State	Published - 2014

Bibliographical note

Publisher Copyright:
Copyright © by SIAM.

Keywords

Coderivatives
Full stability of local minimizers
Nondegeneracy
Quadratic growth
Second-order cone programming
Second-order subdifferentials
Strong regularity
Variational analysis

ASJC Scopus subject areas

Software
Theoretical Computer Science

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10.1137/130928637

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title = "Full stability of locally optimal solutions in second-order cone programs",

abstract = "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.",

keywords = "Coderivatives, Full stability of local minimizers, Nondegeneracy, Quadratic growth, Second-order cone programming, Second-order subdifferentials, Strong regularity, Variational analysis",

author = "Mordukhovich, {Boris S.} and Outrata, {Jiri V.} and Sarabi, {M. Ebrahim}",

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year = "2014",

doi = "10.1137/130928637",

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volume = "24",

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journal = "SIAM Journal on Optimization",

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T1 - Full stability of locally optimal solutions in second-order cone programs

AU - Mordukhovich, Boris S.

AU - Outrata, Jiri V.

AU - Sarabi, M. Ebrahim

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Coderivatives

KW - Full stability of local minimizers

KW - Nondegeneracy

KW - Quadratic growth

KW - Second-order cone programming

KW - Second-order subdifferentials

KW - Strong regularity

KW - Variational analysis

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DO - 10.1137/130928637

M3 - Article

AN - SCOPUS:84919820014

SN - 1052-6234

VL - 24

SP - 1581

EP - 1613

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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