A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer---Burmeister merit function

Authors:
Jianguang Zhu;Hongwei Liu;Changhe Liu;Weijie Cong
Affiliations:
Department of Mathematics, Xidian University, Xi'an, China 710071;Department of Mathematics, Xidian University, Xi'an, China 710071;Department of Mathematics, Xidian University, Xi'an, China 710071 and Department of Applied Mathematics, Henan University of Science and Technology, Luoyang, China;School of Science, Xi'an University of Posts and Telecommunications, Xi'an, China
Venue:
Numerical Algorithms
Year:
2011

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Abstract

In this paper, we propose a new generalized penalized Fischer---Burmeister merit function, and show that the function possesses a system of favorite properties. Moreover, for the merit function, we establish the boundedness of level set under a weaker condition. We also propose a derivative-free algorithm for nonlinear complementarity problems with a nonmonotone line search. More specifically, we show that the proposed algorithm is globally convergent and has a locally linear convergence rate. Numerical comparisons are also made with the merit function used by Chen (J Comput Appl Math 232:455---471, 2009), which confirm the superior behaviour of the new merit function.