本文選題：交替方向乘子法　切入點(diǎn)：收斂速率　出處：《山西大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年04期 　論文類型：期刊論文

【摘要】：交替方向乘子法(Alternating Direction Method of Multipliers,簡稱ADMM)已經(jīng)成為求解大規(guī)模結(jié)構(gòu)性優(yōu)化問題的有效方法。盡管已經(jīng)有較多關(guān)于ADMM算法收斂性的研究,但關(guān)于該算法參數(shù)對收斂性影響的定量表示仍須進(jìn)一步研究,已有的結(jié)果中僅是在實(shí)驗(yàn)中憑經(jīng)驗(yàn)對步長進(jìn)行選取。文章研究ADMM算法l_1正則化最小的一個重要問題Lasso的收斂因子。研究發(fā)現(xiàn)解的形式可用軟閾值算子表示,分析發(fā)現(xiàn)軟閾值的三種情況可以等價轉(zhuǎn)化成算法收斂因子的兩種情況,然后通過最小化收斂因子解出最優(yōu)的步長。實(shí)驗(yàn)表明,應(yīng)用該方法選出的步長,其相應(yīng)算法的收斂速度明顯快于其他選取步長的情況。此外,將該方法應(yīng)用到壓縮感知問題,給出了一個計(jì)算最優(yōu)步長的近似值策略,獲得了較好的實(shí)驗(yàn)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.
【作者單位】： 中國計(jì)量大學(xué)理學(xué)院;
【基金】：國家自然科學(xué)基金(61672477;61571510)
【分類號】：TN911.7

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1 陳光明;基于線性規(guī)劃譯碼的交替方向乘子法算法研究[D];西安電子科技大學(xué);2015年

2 王珂;基于PDR技術(shù)的行進(jìn)人員步態(tài)檢測與方向位移計(jì)算[D];天津大學(xué);2016年

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本文編號：1566743