On the Application of the SCD Semismooth* Newton Method to Variational Inequalities of the Second Kind

0569924 - ÚTIA 2023 RIV NL eng J - Journal Article
Gfrerer, H. - Outrata, Jiří - Valdman, Jan
On the Application of the SCD Semismooth* Newton Method to Variational Inequalities of the Second Kind.
Set-Valued and Variational Analysis. Roč. 30, č. 4 (2022), s. 1453-1484. ISSN 1877-0533. E-ISSN 1877-0541
R&D Projects: GA ČR GF21-06569K
Institutional support: RVO:67985556
Keywords : Newton method * Semismoothness∗ * Superlinear convergence * Global convergence * Generalized equation * Coderivatives
OECD category: Pure mathematics
Impact factor: 1.6, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2023/MTR/valdman-0569924.pdf https://link.springer.com/article/10.1007/s11228-022-00651-2

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.
Permanent Link: https://hdl.handle.net/11104/0341243