Smoothing Levenberg-Marquardt algorithm for solving non-Lipschitz absolute value equations

YILMAZ N., Kayacan A.

Journal of Applied Analysis, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1515/jaa-2022-1025
  • Journal Name: Journal of Applied Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, ABI/INFORM, zbMATH
  • Keywords: Non-Lipschitz absolute value equations, smoothing techniques, Levenberg-Marquardt algorithm, GENERALIZED NEWTON METHOD, NEURAL-NETWORK, VERTICAL-BAR, COMPLEMENTARITY, NONSMOOTH
  • Süleyman Demirel University Affiliated: Yes

Abstract

© 2023 Walter de Gruyter GmbH, Berlin/Boston 2023.In this study, we concentrate on solving the problem of non-Lipschitz absolute value equations (NAVE). A new Bezier curve based smoothing technique is introduced and a new Levenberg-Marquardt type algorithm is developed depending on the smoothing technique. The numerical performance of the algorithm is analysed by considering some well-known and randomly generated test problems. Finally, the comparison with other methods is illustrated to demonstrate the efficiency of the proposed algorithm.