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.
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This work is supported by the National Natural Science Foundation of China 61072144.
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Zhu, J., Liu, H., Liu, C. et al. A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer–Burmeister merit function. Numer Algor 58, 573–591 (2011). https://doi.org/10.1007/s11075-011-9471-8
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DOI: https://doi.org/10.1007/s11075-011-9471-8