依赖凝聚函数求解非线性互补问题的一种微分方程方法  

A Differential Equation Approach to Solving Nonlinear Complementarity Problem Based on Aggregate Function

作　　者：周丽美[1] 

机构地区：[1]青岛理工大学数学系

出　　处：《数学的实践与认识》2006年第2期238-243,共6页Mathematics in Practice and Theory

基　　金：青岛理工大学博士基金资助(C2005-115)

摘　　要：利用凝聚函数一致逼近非光滑极大值函数的性质,将非线性互补问题转化为参数化光滑方程组.然后,对此方程组给出了一种微分方程解法,并且证明了非线性互补问题的解是微分方程系统的渐进稳定平衡点.在适当的假设条件下,证明了所给出的算法具有二次收敛速度.数值结果表明了此算法的有效性.By using a smooth aggregate function to approximate the non-smooth max-type function, nonlinear complementarity problem can be treated as a family of parameterized smooth equations. Then, a differential equation approach is proposed to solve such a system. It is proven that the solution of the nonlinear complementarity problem is an asymptotically stable equilibrium point of the proposed differential system. Under mild hypothesis, the local quadratic rate of this algortbm is proved, and illustrative examples are given.

关 键 词：非线性互补问题 微分方程 凝聚函数 渐进稳定 二次收敛 

分 类 号：O241.8[理学—计算数学]