| 广义非线性互补问题的非光滑牛顿算法 |
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| 引用本文： | 李梅霞,田治平. 广义非线性互补问题的非光滑牛顿算法[J]. 潍坊学院学报, 2011, 11(6): 6-10 |
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| 作者姓名： | 李梅霞 田治平 |
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| 作者单位： | 1. 潍坊学院,山东潍坊,261061
2. 山东科技职业学院,山东潍坊,261053 |
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| 基金项目： | 国家自然科学基金资助项目，山东省自然科学基金资助项目 |
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| 摘 要： | 研究了一类在多项式锥上的广义非线性互补问题。借助罚FB互补函数建立了该类问题的非光滑方程，提出了求解该方程的非光滑牛顿算法，证明了与互补函数有关的稳定点即为广义非线性互补问题的解。在较弱的条件下给出了牛顿算法的全局和超线性收敛性。
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| 关 键 词： | 广义非线性互补问题 罚FB互补函数 稳定点 超线性收敛 |
A Nonsmooth Newton Method for Solving the Generalized Nonlinear Complementarity Problem |
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| LI Mei-xia,TIAN Zhi-ping. A Nonsmooth Newton Method for Solving the Generalized Nonlinear Complementarity Problem[J]. Journal of Weifang University, 2011, 11(6): 6-10 |
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| Authors: | LI Mei-xia TIAN Zhi-ping |
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| Affiliation: | LI Mei-xia,TIAN Zhi-ping(Weifang University,Weifang 261061,China,Shandong Vocational College of Science & Technology,Weifang 261053,China) |
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| Abstract: | In this paper, the generalized nonlinear complementarity problem （abbr. GNCP）defined on a polyhedral cone is studied. Based on a penalized FB NCP--function a system of nonsmooth equations is built and the nonsmooth Newton algorithm is presented for solving this system. We prove that the stationary points of the penalized FB merit function are the so-lution of the GNCP. Under mild assumptions, we show that the Newton algorithm is both globally and superlinearly convergent. |
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| Keywords: | GNCP penalized FB NCP-- function stationary point superlinear convergence |
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