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On Lipschitzian properties of implicit multifunctions
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SYSNO ASEP 0467536 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Lipschitzian properties of implicit multifunctions Author(s) Gfrerer, H. (AT)
Outrata, Jiří (UTIA-B) RID, ORCIDNumber of authors 2 Source Title SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234
Roč. 26, č. 4 (2016), s. 2160-2189Number of pages 30 s. Publication form Print - P Language eng - English Country US - United States Keywords solution map ; calmness ; Aubin property ; directional limiting coderivative Subject RIV BA - General Mathematics R&D Projects GA15-00735S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000391853600008 EID SCOPUS 85007227339 DOI 10.1137/15M1052299 Annotation This paper is devoted to the development of new sufficient conditions for the calmness
and the Aubin property of implicit multifunctions. As the basic tool we employ the directional
limiting coderivative which, together with the graphical derivative, enables a fine analysis of the
local behavior of the investigated multifunction along relevant directions. For verification of the
calmness property, in addition, a new condition has been discovered which parallels the missing
implicit function paradigm and permits us to replace the original multifunction by a substantially
simpler one. Moreover, as an auxiliary tool, a handy formula for the computation of the directional
limiting coderivative of the normal-cone map with a polyhedral set has been derived which perfectly
matches the framework of [A. L. Dontchev and R. T. Rockafellar, SIAM J. Optim., 6 (1996),
pp. 1087-1105]. All important statements are illustrated by examples.Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2017
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