带有P0函数的非线性互补问题的一个新的非内点连续算法

数学物理学报 ›› 2011, Vol. 31 ›› Issue (1): 229-238.

带有P₀函数的非线性互补问题的一个新的非内点连续算法

房亮^1,2,贺国平^2,3, 王永丽³

1.泰山学院数学与系统科学学院山东泰安 271021;2.海交通大学数学系上海 200240;3.东科技大学信息科学与工程学院山东青岛 266510

收稿日期:2008-12-11 修回日期:2009-12-29 出版日期:2011-02-25 发布日期:2011-02-25
基金资助:
国家自然科学基金(10571109, 10971122)和山东省自然科学基金(Y2008A01)资助规划常规性课题(06CGYJ21YBQ)资助

A New Non-interior-point Continuation Method for Nonlinear Complementarity Problem with P₀-function

FANG Liang^1,2, HE Guo-Ping^2,3, WANG Yong-Li³

1.College of Mathematics and System Science, Taishan University, Shandong Tai'an 271021|2.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240|3.College of Information Science and Engineering, Shandong University of Science and Technology, Shandong Qingdao 266510266510

Received:2008-12-11 Revised:2009-12-29 Online:2011-02-25 Published:2011-02-25
Supported by:
国家自然科学基金(10571109, 10971122)和山东省自然科学基金(Y2008A01)资助规划常规性课题(06CGYJ21YBQ)资助

摘要/Abstract

摘要：

研究带有P₀函数的非线性互补问题. 基于一个新的光滑函数, 把问题近似成参数化的光滑方程组, 并且给出一个新的非内点连续算法. 所给算法在每步迭代只需要求解一个线性方程组和执行一次Armijo类型的线搜索. 在不需要严格互补条件的情况下, 证明了算法是全局收敛和超线性收敛的. 并且, 在一个较弱的条件下该算法具有局部二阶收敛性. 数值实验证实了算法的可行性和有效性.

关键词: 非线性互补, 非内点连续算法, P₀ -函数, 强制性, 全局收敛

Abstract:

In this paper, nonlinear complementarity problem with $P_0$-function is studied. Based on a new smoothing function,the problem is approximated by a family of parameterized smooth equations and a new non-interior-point continuation method is presented for solving it. At each iteration, the proposed algorithm only need to solve a system of linear equations and perform only one Armijo-type line search. The algorithm is proved to be globally as well as locally superlinearly convergent without strict complementarity. Moreover, the quadratic convergence rate can be achieved under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm.

Key words: Nonlinear complementarity, Non-interior-point continuation method, P₀-function, Coerciveness, Global
convergence

中图分类号:

90C25

房亮, 贺国平, 王永丽. 带有P₀函数的非线性互补问题的一个新的非内点连续算法[J]. 数学物理学报, 2011, 31(1): 229-238.

FANG Liang, HE Guo-Ping, WANG Yong-Li. A New Non-interior-point Continuation Method for Nonlinear Complementarity Problem with P₀-function[J]. Acta mathematica scientia,Series A, 2011, 31(1): 229-238.

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带有P₀函数的非线性互补问题的一个新的非内点连续算法

A New Non-interior-point Continuation Method for Nonlinear Complementarity Problem with P₀-function

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