【摘要】：對(duì)稱的交替方向乘子法(ADMM)是Peaceman-Rachford分裂方法的一個(gè)應(yīng)用。原始的對(duì)稱交替方向乘子法是經(jīng)驗(yàn)性的,理論上并不能保證它的收斂性。最近,何炳生等人(2016)在對(duì)稱的交替方向乘子法中采用不同的步長(zhǎng)來(lái)更新乘子,并證明了它的收斂性。他們使用Glowinski的大步長(zhǎng)來(lái)更新拉格朗日乘子,使得此方法變得更加靈活。在本文中,我們?cè)谄涓鲁跏甲兞康淖訂?wèn)題中增加了半正定的鄰近點(diǎn)項(xiàng),得到了仍然能夠使用Glowinski的大步長(zhǎng)來(lái)更新拉格朗日乘子的結(jié)論。我們證明了帶有鄰近點(diǎn)項(xiàng)的交替方向乘子法的收斂性和在遍歷意義下具有O(1/t)的收斂率。最后,我們用數(shù)值實(shí)驗(yàn)說(shuō)明了選擇大步長(zhǎng)的優(yōu)勢(shì)和該方法的有效性。
[Abstract]:The symmetric alternating direction multiplier method (ADMM) is an application of the Peaceman-Rachford splitting method. The original symmetric alternating direction multiplier method is empirical and cannot guarantee its convergence theoretically. Recently, he Bingsheng et al. (2016) used different steps to update multipliers in symmetric alternating direction multiplier method, and proved its convergence. They used the big steps of Glowinski to update Lagrangian multipliers, making the approach more flexible. In this paper, we add semi-definite neighbor term to the sub-problem of updating initial variable, and obtain the conclusion that we can still update Lagrangian multipliers by using the large step length of Glowinski. We prove the convergence of the alternating direction multiplier method with adjacent point term and the convergence rate of O (1) in the sense of ergodic. Finally, numerical experiments are used to illustrate the advantages of large step selection and the effectiveness of this method.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O224
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本文編號(hào)：2438341