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运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 53-58.

• 运筹学 • 上一篇    下一篇

非光滑非线性互补问题的牛顿法

 高岩   

  • 出版日期:2011-06-15 发布日期:2011-06-15

 A Newton Method for  a  Nonsmooth Nonlinear　Complementarity　Problem

 GAO  Yan   

  • Online:2011-06-15 Published:2011-06-15
  • Supported by:

    Supported by the   National Science Foundation of China (No. 10671126), Shanghai Municipal Committee of Science and Technology (No. 10550500800) and Shanghai Leading Discipline Project (No. S30501)

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摘要：  研究了非光滑的非线性互补问题. 首先将非光滑的非线性互补问题转化为一个非光滑方程组,然后用牛顿法求解这个非光滑方程组. 在该牛顿法中,每次迭代只需一个原始函数B-微分中的一个元素. 最后证明了该牛顿法的超线性收敛性.

关键词: 非线性互补问题, 非光滑分析, 优化,牛顿法

Abstract: This paper is devoted to a nonlinear　complementarity problem with nonsmooth data. The  nonlinear　complementarity problem is reformulated as a system of nonsmooth　equations. Then, a Newton method for solving the nonsmooth equations　is proposed. In each iteration of the Newton method, an element of　the B-differential of related functions, not nonlinear　complementarity function, is required. The superlinear convergence　is shown.

Key words: nonlinear complementarity problem, nonsmooth analysis, optimization,  , Newton methods

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