- Title
- On the application of the SCD semismooth* newton method to variational inequalities of the second kind
- Creator
- Gfrerer, Helmut; Outrata, Jiri; Valdman, Jan
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/190383
- Identifier
- vital:17580
- Identifier
-
https://doi.org/10.1007/s11228-022-00651-2
- Identifier
- ISSN:1877-0533 (ISSN)
- Abstract
- The paper starts with a description of SCD (subspace containing derivative) mappings and the SCD Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm which exhibits locally superlinear convergence. Thereafter we suggest several globally convergent hybrid algorithms in which one combines the SCD Newton method with selected splitting algorithms for the solution of monotone variational inequalities. Finally, we demonstrate the efficiency of one of these methods via a Cournot-Nash equilibrium, modeled as a variational inequality of the second kind, where one admits really large numbers of players (firms) and produced commodities. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
- Publisher
- Springer Science and Business Media B.V.
- Relation
- Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1453-1484; https://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
- Copyright @ 2022, The Author(s)
- Subject
- 4901 Applied mathematics; 4904 Pure mathematics; Coderivatives; Generalized equation; Global convergence; Newton method; Semismoothness∗; Superlinear convergence
- 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. The research of the third author was supported by the Grant Agency of the Czech Republic, Project 21-06569K.
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