本文關(guān)鍵詞： 凸規(guī)劃 對(duì)稱交替方向法 鄰近點(diǎn) 大步長(zhǎng)　出處：《南京大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文研究具有大步長(zhǎng)鄰近點(diǎn)的對(duì)稱交替方向法的收斂性與取較大步長(zhǎng)因子時(shí)算法的數(shù)值表現(xiàn)。對(duì)稱交替方向法在一次迭代中,更新對(duì)偶變量λ兩次,故交替方向法可以視為對(duì)稱交替方向法的特例。在迭代中,更新對(duì)偶變量的計(jì)算量小,而求解x,y子問(wèn)題的計(jì)算量大。所以如果能通過(guò)增加對(duì)偶變量的更新次數(shù)來(lái)減少求解x,y子問(wèn)題的次數(shù),那么很有可能可以提升算法的效率。鑒于經(jīng)典的對(duì)稱交替方向法在求解具有兩個(gè)算子的可分凸規(guī)劃問(wèn)題上數(shù)值表現(xiàn)優(yōu)越,但其收斂性在理論上沒(méi)有保證,所以我們通過(guò)引入步長(zhǎng)因子來(lái)考慮帶步長(zhǎng)因子的對(duì)稱交替方向法的收斂性分析。此前,何老師等通過(guò)引入步長(zhǎng)因子,考慮了對(duì)稱交替方向法的收斂性。本文在此基礎(chǔ)上,將對(duì)稱交替方向法的步長(zhǎng)因子范圍擴(kuò)大。我們證明了在該范圍內(nèi)對(duì)稱交替方向法的全局收斂性。此外,為了使算法更加靈活,我們?cè)谧訂?wèn)題中引入了鄰近項(xiàng)。更多的交替方向法型算法可以被視為對(duì)稱交替方向法的特例。并通過(guò)實(shí)驗(yàn)說(shuō)明了帶較大步長(zhǎng)因子的對(duì)稱交替方向法的數(shù)值有效性。
[Abstract]:In this paper, the convergence of symmetric alternating direction method with large step size adjacent points and the numerical performance of the algorithm with large step size factor are studied. In one iteration, the symmetric alternating direction method updates the dual variable 位 twice. Therefore, the alternating direction method can be regarded as a special case of the symmetric alternating direction method. Therefore, if we can reduce the number of times to solve xy subproblem by increasing the number of updates of dual variables, It is possible to improve the efficiency of the algorithm. Whereas the classical symmetric alternating direction method is superior in solving separable convex programming problems with two operators, its convergence is not guaranteed in theory. So we consider the convergence analysis of symmetric alternating direction method with step size factor by introducing step size factor. Previously, he et al. considered the convergence of symmetric alternating direction method by introducing step size factor. The step size factor range of symmetric alternating direction method is expanded. We prove the global convergence of symmetric alternating direction method in this range. In addition, in order to make the algorithm more flexible, We introduce the adjacent term into the subproblem. More alternative direction method can be regarded as a special case of symmetric alternating direction method. The numerical validity of the symmetric alternating direction method with large step size factor is illustrated by experiments.
【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)】：O221
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本文編號(hào)：1512844