非线性二阶锥互补问题的低阶罚函数算法（英文）  

Lower-Order Penalty Approach for Second-Order Cone Nonlinear Complementarity Problems

作　　者：郝自军 张玉栋[2] 余国林 HAO Zijun;ZHANG Yudong;YU Guolin(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;Zaozhuang Vocational College of Science and Technology,Tengzhou 277500,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 [2]枣庄科技职业学院,山东滕州277500

出　　处：《应用数学》2020年第1期100-110,共11页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11661002,11601012);the College Scientific Research Fund of Ningxia(NGY2016136);the Key Project of North Minzu University(ZDZX201804);the First-class Disciplines Foundation of Ningxia(NXYLXK2017B09)

摘　　要：本文研究非线性二阶锥互补问题的一般低阶罚函数算法.并将非线性二阶锥互补问题转化为序列非线性方程组.在一定条件下,当罚因子趋向于无穷时,获得序列非线性方程组的解序列以指数速度收敛于原始非线性二阶锥互补问题的解,推广了幂罚函数算法求解非线性二阶锥互补问题的结果.数值实验结果说明了算法的有效性.Lower-order penalty approach,which is the extension of the power penalty approach,is proposed for solving second-order cone nonlinear complementarity problems(SOC-NCPs).And the SOC-NCP is converted to asymptotic nonlinear equations.The merit of this approach shows that the solution sequence of the asymptotic nonlinear equations converges to the solution of the SOC-NCP at an exponential rate when the penalty parameter tends to positive infinity under mild assumptions.Numerical results are reported to examine the efficiency of the proposed approach.

关 键 词：二阶锥 非线性互补问题 低阶罚算法 指数收敛速度 

分 类 号：O221[理学—运筹学与控制论]