基于投影算子的求解线性互补问题的微分方程方法  

A Differential Equation Method Based on Projection Operator for Linear Complementarity Problems

作　　者：李阳 丁淑妍 刘红梅 LI Yang;DING Shu-yan;LIU Hong-mei(School of Science, Dalian Minzu University, Dalian Liaoning 116650, China)

机构地区：[1]大连民族大学理学院,辽宁大连116650

出　　处：《大连民族大学学报》2019年第1期78-80,共3页Journal of Dalian Minzu University

基　　金：国家自然科学基金青年基金项目(11501080)

摘　　要：给出了一种求解线性互补问题的微分方程方法。首先利用投影算子构造了线性互补问题的能量函数;其次利用该函数构造了微分方程系统,并证明了该系统的平衡点集等于线性互补问题的解集;接着给出了微分方程系统的稳定性证明及算法的全局收敛性证明;最后利用数值算例验证了算法的有效性。This paper provides a differential equation method for solving linear complementarity problems.Firstly,based on a projection operator,an energy function is constructed.Secondly,a differential equation system is provided,which is constructed by the energy function above.And it’s proved that the equilibrium point set of the differential equation system is equal to the solution set of the linear complementarity problem.Thirdly,the stability of the differential equation system and the global convergence of this algorithm are proved.Finally,two numerical examples validate the effectiveness of this algorithm.

关 键 词：线性互补问题 微分方程方法 全局收敛 

分 类 号：O221.1[理学—运筹学与控制论]