On a semismooth* Newton method for solving generalized equations

2019/04/19 by Helmut Gfrerer, Gfrerer, H., Jan Outrata +1 · 3 citations
Computer Science · Mathematics · #65K10 #65K15 #90C33 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1904.09167

openalex publication_date 2019/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 multi-valued part of the considered GE. The method is based on the new notion of semismoothness^* which, together with a suitable regularity condition, ensure 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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