A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P0-function

Authors:
Bilian Chen;Changfeng Ma
Affiliations:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China 350007 and Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Sh ...;School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China 350007
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

In this paper, we propose a new smoothing Broyden-like method for solving nonlinear complementarity problem with P 0 function. The presented algorithm is based on the smoothing symmetrically perturbed minimum function 驴(a, b) = min{a, b} and makes use of the derivative-free line search rule of Li et al. (J Optim Theory Appl 109(1):123---167, 2001). Without requiring any strict complementarity assumption at the P 0-NCP solution, we show that the iteration sequence generated by the suggested algorithm converges globally and superlinearly under suitable conditions. Furthermore, the algorithm has local quadratic convergence under mild assumptions. Some numerical results are also reported in this paper.