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On a Semismooth* Newton Method for Solving Generalized Equations
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SYSNO ASEP 0541231 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On a Semismooth* Newton Method for Solving Generalized Equations Author(s) Gfrerer, H. (AT)
Outrata, Jiří (UTIA-B) RID, ORCIDSource Title SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234
Roč. 31, č. 1 (2021), s. 489-517Number of pages 29 s. Publication form Print - P Language eng - English Country US - United States Keywords Newton method ; semismoothness* ; superlinear convergence ; generalized equation ; coderivatives Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA17-04301S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UTIA-B - RVO:67985556 UT WOS 000636678300020 EID SCOPUS 85102060544 DOI 10.1137/19M1257408 Annotation In the paper, a Newton-type method for the solution of generalized equations (GEs) is derived, where the linearization concerns both the single-valued and the multivalued part of the considered GE. The method is based on the new notion of semismoothness*, which, together with a suitable regularity condition, ensures the local superlinear convergence. An implementable version of the new method is derived for a class of GEs, frequently arising in optimization and equilibrium models.
Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2022 Electronic address https://epubs.siam.org/doi/10.1137/19M1257408
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