On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction

2022/05/30 by H. Gfrerer, M. Mandlmayr, Gfrerer, H. +5
Engineering · Mathematics · #65K10 #65K15 #90C33 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Learning Control Systems #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2205.15129

openalex publication_date 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper, a variant of the \ssstar Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild regularity requirement, the method exhibits (locally) superlinear convergence behavior. From the main conceptual algorithm, two implementable variants are derived whose efficiency is tested via a generalized equation modeling a discretized static contact problem with Coulomb friction.

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