BFGS校正拟牛顿法解决大规模信号恢复问题  

LARGE-SCALE SPARSE SIGNAL RECOVERY BY QUASI-NEWTON METHOD OF BFGS CORRECTION

作　　者：陈凤华[1] 李双安[1] 

机构地区：[1]河南理工大学万方科技学院,河南郑州451400

出　　处：《数学杂志》2015年第3期727-734,共8页Journal of Mathematics

基　　金：国家自然科学基金(11361018);广西杰出青年基金(2012GXSFFA060003);河南省教育厅科学技术研究重点项目(12B110011)

摘　　要：本文采用BFGS校正拟牛顿法研究了大规模信号恢复问题min{u 1:Au=b},这个问题通常被转化为1正则化最小二乘问题.利用Nesterov光滑化技术对u 1进行光滑化处理,原问题被转化为无约束光滑凸规划问题,最后获得了较好的数值实验结果,实验结果表明用BFGS校正拟牛顿法解决大规模信号恢复问题是可行的.In this paper we study the lage-scale sparse signal recovery problem such as min{｜｜u｜｜1 ： Au = b}, adopting the quasi-Newton method of BFGS correction. This problem is usually transformed into l1-regularized least-squares programs. By using the Nesterov＇s smoothing method for ｜｜u｜｜1, the original problem is transformed into an unconstrained smoothing convex programming. Further the numerical solution of the algorithm is obtained. Preliminary numerical results show that our algorithm is feasible for solving large-scale sparse signal recovery problems.

关 键 词：压缩感知 BFGS校正 拟牛顿法 稀疏信号 光滑优化 

分 类 号：O221.1[理学—运筹学与控制论]