可分离二次规划问题的自适应交替方向乘子法  

A self-adaptive alternating direction multiplier method for separable quadratic programming problems

作　　者：唐瑜 张守贵 TANG Yu;ZHANG Shougui(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆理工大学学报（自然科学）》2022年第5期284-289,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11971085);重庆市自然科学基金项目(cstc2020jcyj-msxmX0066);重庆市高校创新研究群体项目(CXQT19018);重庆市研究生教育优质课程项目(201949);重庆市研究生教育教学改革研究项目(yjg213071)。

摘　　要：利用增广拉格朗日乘子法和自适应法则,得到求解具有等式约束的可分离二次规划问题的自适应交替方向乘子法。将问题转化为用2个块变量和增广拉格朗日函数表示的极小值问题。采用交替方向乘子法求解,每次迭代由2个二次规划子问题和更新拉格朗日乘子组成。为了改进算法性能,用自适应法则自动近似罚参数。证明了算法收敛性,给出了算法的具体应用,数值结果验证了自适应算法的有效性。This paper propose a self-adaptive alternating direction method of multiplier for separable quadratic programming problems with equality constraints,which uses the augmented Lagrange multiplier method and a self-adaptive rule.By reformulating the problem as a minimum problem with two blocks of variables and the augmented Lagrange function,an alternating direction method of multipliers is suggested to solve the problem,and each iteration consists of two optimization subproblems and updating the Lagrangian multiplier.To improve the performance of the method,the self-adaptive rule is used to approximate the parameter automatically.We then show the convergence of the method and give its application in detail.Finally,the numerical results are proposed to illustrate the efficiency of the method with the self-adaptive method.

关 键 词：二次规划问题 等式约束 交替方向乘子法 增广拉格朗日函数 自适应法则 

分 类 号：O221[理学—运筹学与控制论]