On Lipschitzian properties of implicit multifunctions

0467536 - ÚTIA 2017 RIV US eng J - Journal Article
Gfrerer, H. - Outrata, Jiří
On Lipschitzian properties of implicit multifunctions.
SIAM Journal on Optimization. Roč. 26, č. 4 (2016), s. 2160-2189. ISSN 1052-6234. E-ISSN 1095-7189
R&D Projects: GA ČR GA15-00735S
Grant - others:Austrian Science Fund(AT) P26132-N25; Australian Research Council(AU) DP160100854
Institutional support: RVO:67985556
Keywords : solution map * calmness * Aubin property * directional limiting coderivative
Subject RIV: BA - General Mathematics
Impact factor: 1.968, year: 2016
http://library.utia.cas.cz/separaty/2016/MTR/outrata-0467536.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0265783