光滑互补函数与互补问题的2-正则解  

Smooth Complementarity Function and 2-Regular Solution of Complementarity Problem

作　　者：俞昊东[1] 徐翠霞[2] 濮定国[1] 

机构地区：[1]同济大学应用数学系 [2]河南科技大学数学与统计学院

出　　处：《河南科技大学学报（自然科学版）》2011年第1期67-71,120,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10771162;10971053);河南省自然科学基金项目(094300510050)

摘　　要：研究了用光滑互补函数将互补问题转化为非线性方程组时产生的正则性问题。光滑互补函数通常会导致再生方程组产生奇异解,而2-正则性条件是解决奇异性问题的一种工具。在分析了光滑互补函数与二次正齐次函数性质的基础上,给出了2-正则性的成立条件。证明了在很弱的条件下,利用二次正齐次的光滑互补函数可使再生方程组的2-正则性严格地弱于原问题的b-正则性,并说明了已有文献采用的互补函数是此类函数的一个特例,还给出了一类新的符合条件的互补函数。In this paper,the regularity problem caused by using smooth NCP functions to reformulate nonlinear complementarity problem to nonlinear equations was studied.Generally,smooth NCP functions will cause singular solutions of the reformulation equations,while the 2-regularity condition is an approach to solve the singularity problem.Based on the analysis of the properties of smooth NCP functions and 2-positive homogeneous functions,the condition under which the 2-regularity condition holds is established.If a 2-positive homogeneous NCP function is used,the 2-regularity of the reformulation equations is strictly weaker than the b-regularity of the original nonlinear complementarity problem.Furthermore,the NCP function used by current papers belongs to the class discussed in this paper,and a new smooth NCP function of the same class is proposed as well.

关 键 词：非线性互补函数 2-正则性 二次正齐次 非线性互补问题 b-正则性 

分 类 号：O221.2[理学—运筹学与控制论]