增广Lagrange方法求解二阶锥约束变分不等式问题  

An augmented Lagrange method for solving second-order cone-constrained variational inequalities

作　　者：刘雨 孙菊贺 王莉 米娜 袁艳红[2] LIU Yu;SUN Juhe;WANG Li;MI Na;YUAN Yanhong(College of Science,Shenyang Aerospace University,Shenyang 110136,China;College of Economics and Management,Taiyuan University of Technology,Taiyuan 030002,China)

机构地区：[1]沈阳航空航天大学理学院,沈阳110136 [2]太原理工大学经济管理学院,太原030002

出　　处：《沈阳航空航天大学学报》2023年第4期72-79,共8页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:11801381)。

摘　　要：应用增广Lagrange方法求解了一类二阶锥约束变分不等式问题。首先,将二阶锥约束变分不等式问题转化为等价的优化问题,从而得到其不同的等价形式;其次,应用投影算子的性质,将二阶锥约束变分不等式问题转化为方程组问题,并针对方程组问题提出了增广Lagrange方法;再次,讨论了算法的全局收敛性,同时对算法的一个特殊情况进行了深入分析,并引入一类非精确牛顿法求解算法中蕴含的子问题;最后,给出3个算例的数值实验结果,验证了算法的可行性。The augmented Lagrange method was applied to solve a class of cone-constrained variational inequalities of second-order.Firstly,the second-order cone-constrained variational inequality problem was transformed into an equivalent optimization problem,and its different equivalent forms were obtained.Secondly,the second-order cone-constrained variational inequality problem was transformed into a system of equations by using the properties of projection operator,and the augmented Lagrange method was proposed for the system of equations.Thirdly,the global convergence of the algorithm was discussed,and a special case of the algorithm was deeply analyzed,and a class of inexact Newton method was introduced to solve the subproblems contained in the algorithm.Finally,three numerical examples were given to verify the feasibility of the algorithm.

关 键 词：二阶锥约束 变分不等式 增广Lagrange法 非精确牛顿法 投影算子 收敛性 

分 类 号：O221.5[理学—运筹学与控制论]