- Title
- On lipschitzian properties of implicit multifunctions
- Creator
- Gfrerer, Helmut; Outrata, Jiri
- Date
- 2016
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154327
- Identifier
- vital:11091
- Identifier
-
https://doi.org/10.1137/15M1052299
- Identifier
- ISSN:10526234
- Abstract
- 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. © 2016 Society for Industrial and Applied Mathematics.
- Publisher
- Society for Industrial and Applied Mathematics Publications
- Relation
- SIAM Journal on Optimization Vol. 26, no. 4 (2016), p. 2160-2189; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Aubin property; Calmness; Directional limiting coderivative; Solution map; Software engineering; Aubin properties; Fine analysis; Implicit function; Implicit multifunctions; Lipschitzian; Nocv1; Polyhedral set; Computer science
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