两项修正PRP共轭梯度算法在稀疏优化中的应用  

APPLICATION OF TWO-TERM MODIFIED PRP CONJUGATE GRADIENT ALGORITHMS IN SPARSE OPTIMIZATION

作　　者：李凯 林彭壮汉 胡子健 程万友 Li Kai;Linpeng Zhuanghan;Hu Zijian;Cheng Wanyou(College of Computer Science,Dongguan University of Technology,Dongguan 523808)

机构地区：[1]东莞理工学院计算机系,东莞523808

出　　处：《高等学校计算数学学报》2024年第2期137-152,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(12271187,11961011,11971106);广东省自然科学基金项目(2022A1515010567);广东省普通高校重点领域专项(2021ZDZX1054)。

摘　　要：1引言近年来,压缩感知成为信号分析与处理领域最为热门的研究课题之一,利用压缩感知的思想,我们可以对原始稀疏信号恢复问题进行深层的研究.信号重建问题可以建模如下:min||x||0s.t.b=Ax,其中x∈R^(n)是需要恢复的原始稀疏信号,||x||0表示x中非零元素的个数.In recent years,the sparse optimization problem has attracted extensive attention in many fields such as scientific research and engineering practice.The conjugate gradient method is suitable for large-scale problems due to its simplicity,low memory,and global convergence.We combine two-term modified conjugate gradient method with a smoothing strategy to solve the sparse optimization problems and establish the global convergence of the algorithm.Finally,we select some representative sparse recovery problems,combine our new algorithm,and design relevant numerical experiments.By comparing with the existing excellent algorithms,it is proved that the new algorithm has better competitiveness.

关 键 词：共轭梯度算法 非零元素 信号分析与处理 压缩感知 信号重建 稀疏信号 稀疏优化 

分 类 号：O221.2[理学—运筹学与控制论]