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On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
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SYSNO ASEP 0557191 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives Author(s) Gfrerer, H. (AT)
Outrata, Jiří (UTIA-B) RID, ORCIDArticle number 125895 Source Title Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 508, č. 2 (2022)Number of pages 37 s. Publication form Print - P Language eng - English Country US - United States Keywords Generalized derivatives ; Second-order theory ; Strong metric (sub)regularity ; Semismoothness⁎ Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GF21-06569K GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UTIA-B - RVO:67985556 UT WOS 000795432700023 EID SCOPUS 85120931541 DOI 10.1016/j.jmaa.2021.125895 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2023 Electronic address https://www.sciencedirect.com/science/article/pii/S0022247X2100977X?via%3Dihub
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