Abstract.
We propose a modified one-step smoothing Newton method for solving nonlinear complementarity problems with P 0-function (P 0-NCP) based on CHKS smoothing function. Our smoothing Newton method solves only one linear system of equations and performs only one line search at each iteration. It is proved that our proposed algorithm has superlinear convergence in absence of strict complementarity assumption at the P 0-NCP solution. Under suitable conditions, the modified algorithm has global linear and local quadratic convergence. Compared to previous literatures, our algorithm has stronger convergence results under weaker conditions.
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Manuscript received: December 2001/Final version received: March 2002
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ID="*" This work was partly supported by the National Natural Science Foundation of China (Grant No. 19971002,79970014), Cross-century Excellent Personnel Award and Teaching & Research Award Program for outstanding Young Teachers in Higher Education Institutions of Ministry of Education, China.
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Zhang, L., Gao, Z. Superlinear/quadratic one-step smoothing Newton method for P0-NCP without strict complementarity. Mathematical Methods of OR 56, 231–241 (2002). https://doi.org/10.1007/s001860200221
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DOI: https://doi.org/10.1007/s001860200221