组基数约束指数跟踪问题的梯度投影算法  

A Projected Gradient Algorithm for Group Cardinality Constrained Index Tracking

作　　者：黄晓鑫 吴景岚 朱文兴[1] HUANG Xiaoxin;WU Jinglan;ZHU Wenxing(College of Mathematics and Computer Science,Fuzhou University,Fuzhou Fujian 350116,China;College of Computer and Control Engineering,Minjiang University,Fuzhou Fujian 350108,China)

机构地区：[1]福州大学数学与计算机科学学院,福建福州350116 [2]闽江学院计算机与控制工程学院,福建福州350108

出　　处：《莆田学院学报》2020年第5期1-7,共7页Journal of putian University

基　　金：国家自然科学基金资助项目(61672005);福建省自然科学基金资助项目(2017J01768)。

摘　　要：研究带组基数约束的指数跟踪问题:首先,基于梯度投影算法和拉格朗日方法,给出迭代子问题的闭式解;其次,据此闭式解,提出一个迭代组软阈值算法,并证明算法在一定条件下最终会收敛到原问题的L-稳定点;最后,结合线搜索、非单调技巧和启发式方法,进一步给出了一个非单调的迭代组软阈值算法,用于迭代求解原问题。数值实验表明算法是有效的。In this paper,we study an index tracking problem with a group cardinality constraint.Firstly,based on the projected gradient algorithm and the Lagrangian method,we derive a closed-form solution to an iterative subproblem.Then based on this closed-form solution,we propose an iterative group soft thresholding algorithm,and prove that it will converge to an L-stationary point of the primal problem under some conditions.Finally,combining this algorithm with line search,nonmonotone trick and heuristic method,we further propose a nonmonotone iterative group soft thresholding algorithm to solve the primal problem iteratively.To show its effectiveness,the algorithm is tested on a set of simulated data of group index tracking.

关 键 词：指数跟踪 组基数 梯度投影算法 迭代组软阈值算法 拉格朗日方法 

分 类 号：O224[理学—运筹学与控制论]