Applied Mathematics and Optimization

, Volume 52, Issue 1, pp 73–92

A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone


DOI: 10.1007/s00245-005-0823-4

Cite this article as:
Wang, Y., Ma, F. & Zhang, J. Appl Math Optim (2005) 52: 73. doi:10.1007/s00245-005-0823-4


In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent. Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented.

GNCPStationary pointSuperlinear convergence

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institute of Operations Research, Qufu Normal University, Rizhao Shandong 276800 People’s Republic of China
  2. 2.Department of Applied Mathematics, The Hong Kong Polytechnic University, KowloonHong Kong
  3. 3.Department of Mathematics, City University of Hong Kong, KowloonHong Kong