On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives

0557191 - ÚTIA 2023 RIV US eng J - Journal Article
Gfrerer, H. - Outrata, Jiří
On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives.
Journal of Mathematical Analysis and Applications. Roč. 508, č. 2 (2022), č. článku 125895. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GF21-06569K
Institutional support: RVO:67985556
Keywords : Generalized derivatives * Second-order theory * Strong metric (sub)regularity * Semismoothness⁎
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2022/MTR/outrata-0557191.pdf https://www.sciencedirect.com/science/article/pii/S0022247X2100977X?via%3Dihub

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.
Permanent Link: http://hdl.handle.net/11104/0331258