Levenberg-marquardt method for absolute value equation associated with second-order cone

Xin He Miao, Kai Yao, Ching Yu Yang, Jein Shan Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the stan-dard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indi-cates that the proposed algorithm could also be a good choice for solving the SOCAVE.

Original languageEnglish
Pages (from-to)47-61
Number of pages15
JournalNumerical Algebra, Control and Optimization
Issue number1
Publication statusPublished - 2022 Mar


  • Absolute value equations
  • Armijo line search
  • Levenberg-Marquardt algorithm
  • Second-order cone

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Control and Optimization
  • Applied Mathematics


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