基于ADMM算法正则化最优步长的研究

发布时间：2018-03-04 18:09

本文选题：交替方向乘子法　切入点：收敛速率　出处：《山西大学学报(自然科学版)》2017年04期 　论文类型：期刊论文

【摘要】：交替方向乘子法(Alternating Direction Method of Multipliers,简称ADMM)已经成为求解大规模结构性优化问题的有效方法。尽管已经有较多关于ADMM算法收敛性的研究,但关于该算法参数对收敛性影响的定量表示仍须进一步研究,已有的结果中仅是在实验中凭经验对步长进行选取。文章研究ADMM算法l_1正则化最小的一个重要问题Lasso的收敛因子。研究发现解的形式可用软阈值算子表示,分析发现软阈值的三种情况可以等价转化成算法收敛因子的两种情况,然后通过最小化收敛因子解出最优的步长。实验表明,应用该方法选出的步长,其相应算法的收敛速度明显快于其他选取步长的情况。此外,将该方法应用到压缩感知问题,给出了一个计算最优步长的近似值策略,获得了较好的实验效果。
[Abstract]:The alternating direction multiplier method (ADMMM) has become an effective method for solving large-scale structural optimization problems, although there have been many studies on the convergence of ADMM algorithms. However, the quantitative representation of the effect of the parameters of the algorithm on convergence still needs to be further studied. In the existing results, the step size is only selected by experience in experiments. In this paper, we study the convergence factor of Lasso, which is an important problem in the minimization of the regularization of ADMM algorithm lStup 1. It is found that the form of solution can be expressed by soft threshold operator. It is found that the three cases of soft threshold can be equivalent to two cases of convergence factor of the algorithm, and then the optimal step size is solved by minimizing the convergence factor. The convergence speed of the corresponding algorithm is obviously faster than that of other selected step sizes. In addition, the proposed algorithm is applied to the compression perception problem, and an approximation strategy for calculating the optimal step size is presented, and the experimental results are satisfactory.
【作者单位】：中国计量大学理学院;
【基金】：国家自然科学基金(61672477;61571510)
【分类号】：TN911.7

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