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Journal Article

On Lipschitzian properties of implicit multifunctions

Gfrerer H., Outrata Jiří

: SIAM Journal on Optimization vol.26, 4 (2016), p. 2160-2189

: P26132-N25, Austrian Science Fund, GA15-00735S, GA ČR, DP160100854, Australian Research Council

: solution map, calmness, Aubin property, directional limiting coderivative

: 10.1137/15M1052299

: http://library.utia.cas.cz/separaty/2016/MTR/outrata-0467536.pdf

(eng): This paper is devoted to the development of new sufficient conditions for the calmness\nand the Aubin property of implicit multifunctions. As the basic tool we employ the directional\nlimiting coderivative which, together with the graphical derivative, enables a fine analysis of the\nlocal behavior of the investigated multifunction along relevant directions. For verification of the\ncalmness property, in addition, a new condition has been discovered which parallels the missing\nimplicit function paradigm and permits us to replace the original multifunction by a substantially\nsimpler one. Moreover, as an auxiliary tool, a handy formula for the computation of the directional\nlimiting coderivative of the normal-cone map with a polyhedral set has been derived which perfectly\nmatches the framework of [A. L. Dontchev and R. T. Rockafellar, SIAM J. Optim., 6 (1996),\npp. 1087-1105]. All important statements are illustrated by examples.

: BA