二阶锥线性互补问题的低阶罚函数算法  

A LOWER ORDER PENALTY METHOD FOR SECOND-ORDER CONE LINEAR COMPLEMENTARITY PROBLEMS

作　　者：赵雯宇[1] 郝自军[1] 余国林[1] ZHAO Wen-yu HAO Zi-jun YU Guo-lin(School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《数学杂志》2017年第2期427-438,共12页Journal of Mathematics

基　　金：国家自然科学基金(11361001;11661002);宁夏自然科学基金(NZ16093);宁夏高等学校科研项目(NGY2016136)

摘　　要：本文研究了二阶锥线性互补问题的低阶罚函数算法.利用低阶罚函数算法将二阶锥线性互补问题转化为低阶罚函数方程组,获得了低阶罚函数方程组的解序列在特定条件下以指数速度收敛于二阶锥线性互补问题解的结果,推广了二阶锥线性互补问题的幂罚函数算法.数值实验结果验证了算法的有效性.In this paper, a lower order penalty method for solving the second-order cone linear complementarity problems is proposed. By this method, the second-order cone linear complementarity problem is transformed into lower order penalty equations. We prove that the solution sequence of the lower order penalty equations converges to the solution of the second-order cone linear complementarity problems at an exponential rate under a mild assumption, which extend the power penalty method for solving this problem. Numerical results demonstrate that our method is efficient.

关 键 词：二阶锥 线性互补问题 低阶罚函数算法 指数收敛速度 

分 类 号：O224[理学—运筹学与控制论] O221.2[理学—数学]