BFGS校正拟牛顿法解决大规模信号恢复问题
LARGE-SCALE SPARSE SIGNAL RECOVERY BYQUASI-NEWTON METHOD OF BFGS CORRECTION

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l1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