Smoothing techniques in solving non-Lipschitz absolute value equations


YILMAZ N., ŞAHİNER A.

International Journal of Computer Mathematics, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1080/00207160.2022.2163388
  • Journal Name: International Journal of Computer Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: absolute value equations, Newton algorithm, non-Lipschitz functions, smoothing algorithm, Smoothing techniques
  • Süleyman Demirel University Affiliated: Yes

Abstract

© 2023 Informa UK Limited, trading as Taylor & Francis Group.In this study, we define for the first time the non-Lipschitz generalization of absolute value equations and concentrate on solving the problem of non-Lipschitz absolute value equations based on smoothing techniques. Two different types of smoothing techniques which are local and global ones are considered in smoothing process of the problem. With the help of these smoothing techniques, the non-Lipschitz absolute value equations are reformulated as a family of parametrized smooth equations. Two new algorithms are developed to solve the problem by the help of smoothing functions. Finally, the numerical experiments have been performed to illustrate the efficiency of the new algorithms.