Abstract and Applied Analysis

Generalized Newton Method for a Kind of Complementarity Problem

Shou-qiang Du

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


A generalized Newton method for the solution of a kind of complementarity problem is given. The method is based on a nonsmooth equations reformulation of the problem by F-B function and on a generalized Newton method. The merit function used is a differentiable function. The global convergence and superlinear local convergence results are also given under suitable assumptions. Finally, some numerical results and discussions are presented.

Article information

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 745981, 5 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Du, Shou-qiang. Generalized Newton Method for a Kind of Complementarity Problem. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 745981, 5 pages. doi:10.1155/2014/745981. https://projecteuclid.org/euclid.aaa/1412278789

Export citation


  • C. Kanzow and M. Fukushima, “Equivalence of the generalized complementarity problem to differentiable unconstrained minimization,” Journal of Optimization Theory and Applications, vol. 90, no. 3, pp. 581–603, 1996.
  • H. Jiang, M. Fukushima, L. Qi, and D. Sun, “A trust region method for solving generalized complementarity problems,” SIAM Journal on Optimization, vol. 8, no. 1, pp. 140–157, 1998.
  • T. de Luca, F. Facchinei, and C. Kanzow, “A semismooth equation approach to the solution of nonlinear complementarity problems,” Mathematical Programming, vol. 75, no. 3, pp. 407–439, 1996.
  • F. Facchinei and C. Kanzow, “A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems,” Mathematical Programming, vol. 76, no. 3, pp. 493–512, 1997.
  • Y. Gao, “Newton methods for solving two classes of nonsmooth equations,” Applications of Mathematics, vol. 46, no. 3, pp. 215–229, 2001.
  • L. Qi and P. Tseng, “On almost smooth functions and piecewise smooth functions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 3, pp. 773–794, 2007.
  • D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, NY, USA, 1982.
  • L. Q. Qi, “Convergence analysis of some algorithms for solving nonsmooth equations,” Mathematics of Operations Research, vol. 18, no. 1, pp. 227–244, 1993.
  • C. Wang, Q. Liu, and C. Ma, “Smoothing SQP algorithm for semismooth equations with box constraints,” Computational Optimization and Applications, vol. 55, no. 2, pp. 399–425, 2013.
  • S.-Q. Du and Y. Gao, “The Levenberg-Marquardt-type methods for a kind of vertical complementarity problem,” Journal of Applied Mathematics, vol. 2011, Article ID 161853, 12 pages, 2011.
  • X. Chen, “Smoothing methods for nonsmooth, nonconvex minimization,” Mathematical Programming, vol. 134, no. 1, pp. 71–99, 2012.
  • X. Chen, L. Qi, and D. Sun, “Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities,” Mathematics of Computation, vol. 67, no. 222, pp. 519–540, 1998. \endinput