An iterative method for solving semismooth equations

  • Authors:

  • Xiaojiao Tong;Dong-Hui Li;Liqun Qi

  • Affiliations:

  • Department of Mathematics, Nanjing University, 210093 Nanjing, China;Institute of Applied Mathematics, Hunan University, Changsha, China;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
  • Year:
  • 2002

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Abstract

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.