求解l_(1)问题的积极集临近牛顿算法

AN ACTIVE SET PROXIMAL NEWTON METHOD FOR l_(1) OPTIMIZATION

本文提出一种基于积极集识别技术的临近牛顿算法用以求解l_(1)问题.该方法的一个优势在于利用了ISTA算法良好的支集辨认性质去确定自由变量和积极集变量,另一个优势在于利用了部分Hessian矩阵的信息去更新自由变量。在适当的条件下,我们证明了所提出的算法在使用非单调线搜索策略情况下是全局收敛的.数值实验证明提出的算法是有效的.

In this paper,based on the active set identification,we propose a Proximal Newton method for l_(1) problems.One advantage of this method is that it uses the good support identification property of the ISTA algorithm to determine the free variables and active set variables,and another advantage is that it uses the information of the partial Hessian matrix to update the free variables.Under appropriate conditions,we demonstrate the global convergence of the algorithm with a nonmonotonic line search strategy.The results of numerical experiments show that our proposed algorithm is effective.