An iterative method for solving semismooth equations

Xiaojiao Tong, Dong Hui Li, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


In this paper, we combine trust region technique with line search technique to develop an iterative method for solving semismooth equations. At each iteration, a trust region subproblem is solved. The solution of the trust region subproblem provides a descent direction for the norm of a smoothing function. By using a backtracking line search, a steplength is determined. The proposed method shares advantages of trust region methods and line search methods. Under appropriate conditions, the proposed method is proved to be globally and superlinearly convergent. In particular, we show that after finitely many iterations, the unit step is always accepted and the method reduces to a smoothing Newton method.
Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 1 Sept 2002


  • Line search
  • Semismooth equation
  • Smoothing function
  • Trust region method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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