- Title
- On a semismooth* Newton method for solving generalized equations
- Creator
- Gfrerer, Helmut; Outrata, Jiri
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176296
- Identifier
- vital:15109
- Identifier
-
https://doi.org/10.1137/19M1257408
- Identifier
- ISBN:1052-6234 (ISSN)
- Abstract
- 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\ast, 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. © 2021 Society for Industrial and Applied Mathematics
- Publisher
- Society for Industrial and Applied Mathematics Publications
- Relation
- SIAM Journal on Optimization Vol. 31, no. 1 (2021), p. 489-517; https://doi.org/10.1137/19M1257408
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © by SIAM
- Rights
- Open Access
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Coderivatives; Generalized equation; Newton method; Semismoothness*; Superlinear convergence
- Full Text
- Reviewed
- Funder
- Last Received by the editors April 19, 2019; accepted for publication (in revised form) October 28, 2020; published electronically February 2, 2021. https://doi.org/10.1137/19M1257408 Funding: 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 17-04301S, and the Australian Research Council, project DP160100854. \dagger Institute of Computational Mathematics, Johannes Kepler University Linz, A-4040 Linz, Austria (helmut.gfrerer@jku.at). \ddagger Institute of Information Theory and Automation, Czech Academy of Sciences, 18208 Prague, Czech Republic, and Centre for Informatics and Applied Optimization, Federation University of Australia, Ballarat, Vic 3350, Australia (outrata@utia.cas.cz).
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