一种改进的积极集共轭梯度法  

An Improved Active Set Conjugate Gradient Method

作　　者：叶建豪 陈鸿升 胡子健 程万友 YE Jianhao;CHEN Hongsheng;HU Zijian;CHENG Wanyou(School of Computer Science and Technology,Dongguan University of Technology,Dongguan 523000,Guangdong,China)

机构地区：[1]东莞理工学院计算机科学与技术学院,广东东莞523000

出　　处：《昆明理工大学学报（自然科学版）》2023年第6期198-206,共9页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金面上项目(11971106).

摘　　要：共轭梯度法是一种被广泛应用于求解无约束大规模最优化问题的方法,其具有内存需求低、迭代简单的特点.而积极集识别技术具有准确识别最优解附近的零分量的强大能力.为了求解压缩感知、信号和图像处理等领域常见的l_(2)-l_(1)问题,提出了一种基于积极集识别技术和两项下降PRP(Polak-Ribiére-Polyak)方法的积极集共轭梯度方法.在每次迭代中,先利用积极集识别技术区分自由变量和积极变量;然后,使用两项下降的PRP方法更新自由变量,同时用d^(k)=-x^(k)和基于梯度的方法更新积极变量.在适当条件下,新算法被证明了具有全局收敛性.在随机产生的数据上进行实验,实验结果表明,相比部分现有的算法,所提方法具有一定的竞争力.The conjugate gradient method is widely used for solving large-scale unconstrained optimization problems and is characterized by its low memory requirements and simple iterations.The active set identification technique has a strong ability to accurately identify zero components near the optimal solution.To solve common l_(2)-l_(1) problems in areas such as compressed sensing,signal,and image processing,this paper proposes an active set conjugate gradient method based on the active set identification technique and the two-term descent Polak-Ribiére-Polyak(PRP)method.In each iteration,the active set identification technique is used to distinguish between free and active variables;then,the two-term descent PRP method is used to update the free variables,while d^(k)=-x^(k) and a gradient-based method are used to update the active variables.Under appropriate conditions,the new algorithm is proven to have global convergence.Experiments conducted on randomly generated data show that,compared to some existing algorithms,the proposed method is competitive.

关 键 词：无约束优化 积极集 压缩感知 PRP方法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]