求解一般l_(1)趋势过滤问题的原始对偶内点法  

A primal dual interior point algorithm for general l_(1) trend filtering problem

作　　者：张体琪 刘勇进 ZHANG Tiqi;LIU Yongjin(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2022年第4期439-446,共8页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金面上资助项目(11871153);福建省自然科学基金面上资助项目(2019J01644)。

摘　　要：针对一般l_(1)趋势过滤问题提出一种原始对偶内点法,首先给出原始对偶内点法的算法框架,并对原始对偶内点法进行收敛性分析和算法复杂度分析.最后,将提出的算法和目前流行的半光滑牛顿增广拉格朗日方法和交替方向乘子法进行对比.实验结果表明:当模型中的参数变化时,原始对偶内点法更加高效和稳健.In this paper,a primal dual interior point algorithm was proposed to solve the general l_(1) trend filtering problem,and the algorithm framework of the primal dual interior point algorithm was given.Then the convergence and complexity of the primal dual interior point algorithm were analyzed.Finally,we compared the proposed algorithm with some state-of-the-art algorithms,such as semismooth Newton based augmented Lagrangian algorithm and alternating direction method of multipliers.The experimental results demonstrated that the primal dual interior point algorithm was more efficient and robust when the parameters in the model change.

关 键 词：一般l_(1)趋势过滤问题 原始对偶内点法 半光滑牛顿增广拉格朗日算法 

分 类 号：O221[理学—运筹学与控制论]