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

0434303 - ÚTIA 2015 RIV US eng J - Journal Article
Mordukhovich, B. S. - Outrata, Jiří - Sarabi, E.
Full Stability of Locally Optimal Solutions in Second-Order Cone Programs.
SIAM Journal on Optimization. Roč. 24, č. 4 (2014), s. 1581-1613. ISSN 1052-6234. E-ISSN 1095-7189
R&D Projects: GA ČR GAP402/12/1309
Grant - others:Australian Research Council(AU) DP-12092508; Australian Research Council(AU) DP-110102011; Portuguese Foundation of Science and Technologies(PT) MAT/11109; USA National Science Foundation(US) DMS-1007132
Institutional support: RVO:67985556
Keywords : variational analysis * second-order cone programming * full stability of local minimizers * nondegeneracy * strong regularity * quadratic growth * second-order subdifferentials * coderivatives
Subject RIV: BA - General Mathematics
Impact factor: 1.829, year: 2014
http://library.utia.cas.cz/separaty/2014/MTR/outrata-0434303.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0239352