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On a Semismooth* Newton Method for Solving Generalized Equations

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    0541231 - ÚTIA 2022 RIV US eng J - Journal Article
    Gfrerer, H. - Outrata, Jiří
    On a Semismooth* Newton Method for Solving Generalized Equations.
    SIAM Journal on Optimization. Roč. 31, č. 1 (2021), s. 489-517. ISSN 1052-6234. E-ISSN 1095-7189
    R&D Projects: GA ČR GA17-04301S
    Institutional support: RVO:67985556
    Keywords : Newton method * semismoothness* * superlinear convergence * generalized equation * coderivatives
    OECD category: Pure mathematics
    Impact factor: 2.763, year: 2021
    Method of publishing: Limited access

    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.

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