- Title
- On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
- Creator
- Gfrerer, Helmut; Outrata, Jiri
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185185
- Identifier
- vital:16628
- Identifier
-
https://doi.org/10.1016/j.jmaa.2021.125895
- Identifier
- ISBN:0022-247X (ISSN)
- Abstract
- The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the graphically Lipschitzian mappings and thus a number of multifunctions, frequently arising in optimization and equilibrium problems. The developed theory makes use of new generalized derivatives, provides us with some calculus rules and reveals a number of interesting connections. In particular, it enables us to construct a modification of the semismooth* Newton method with improved convergence properties and to derive a generalization of Clarke's Inverse Function Theorem to multifunctions together with new efficient characterizations of strong metric (sub)regularity and tilt stability. © 2021 The Author(s)
- Publisher
- Academic Press Inc.
- Relation
- Journal of Mathematical Analysis and Applications Vol. 508, no. 2 (2022), p.; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2021 The Author(s)
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; 4904 Pure mathematicsGeneralized derivatives; Second-order theory; Semismoothness⁎; Strong metric (sub)regularity
- Full Text
- Reviewed
- Funder
- The research of the first author was supported by the Austrian Science Fund (FWF) under grant P29190-N32 . The research of the second author was supported by the Grant Agency of the Czech Republic , Project 21-06569K , and the Australian Research Council , Project DP160100854
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