求解非线性互补问题的微分方程方法(英文)  

A Differential Equation Approach to Solving Nonlinear Complementarity Problems

作　　者：周丽美[1] 张立卫[2] 贺素香[3] 

机构地区：[1]青岛理工大学理学院,青岛2116033 [2]大连理工大学应用数学系,大连116024 [3]武汉理工大学理学院,武汉430070

出　　处：《运筹学学报》2005年第3期8-16,共9页Operations Research Transactions

基　　金：Supported by the Funds of Ministry of Education of China for PhD Units under No. 200201410L3the National Natural Science Foundation of China under project grant No.10471015

摘　　要：本文构造了一种求解非线性互补问题的微分方程方法.在一定条件下,证明了微分方程系统的平衡点是非线性互补问题的解并且基于一般微分方程系统的数值积分建立了一个数值算法.在适当的条件下,证明了此算法产生的序列解是收敛的,本文最后给出了数值结果,该结果表明了此微分方程方法的有效性.In this paper, a differential equation approach is constructed to solve nonlinear complementarity problems. It is proved that equilibrium solutions of this differential system are solutions to the complementarity problem and a numerical algorithm is given based on the numerical integration of the system of ordinary differential equations. The convergence theorem is established for the numerical algorithm applied to the problem satisfying some assumptions. Some numerical results are reported to illustrate the efficiency of the differential equation approach.

关 键 词：运筹学 微分方程方法 非线性互补问题 非线性互补问题 微分方程系统 求解 数值算法 数值积分 数值结果 平衡点 证明 收敛 

分 类 号：O221.2[理学—运筹学与控制论] O175.14[理学—数学]