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基于广义近似交替方向乘子法求解可分离凸优化问题
Solving Separable Convex Optimization Problem Based on Generalized Proximal Alternating Direction Method of Multipliers

DOI: 10.12677/PM.2021.114062, PP. 485-495

Keywords: 广义近似交替方向乘子法，可分离凸优化，随机加速，全局收敛
Generalized-Proximal Alternating Direction Method of Multipliers, Separable Convex Optimization, Random Acceleration, Global Convergence

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Abstract:

本文提出了一种广义近似交替方向乘子法(gPADMM)来求解可分离凸优化问题。和近似邻近点算法(APPA)和扩展邻近交替方向方法(ePADM)相比，新算法不仅更新自定义矩阵的结构，而且引入随机变量进行随机加速更新步长，从而克服了旧算法固定步长的不灵活性。在某些适当的假设条件下，本文证明了新算法的全局收敛性，并且初步数值实验表明该算法是有效的，收敛速度比旧算法更快。
In this paper, we propose a generalized-proximal alternating direction method of multipliers (gPADMM) for separable convex optimization problem. Compared with the approximate proximal point algorithm (APPA) and the extend proximal alternating directions method (ePADM), the new algorithm not only updates the structure of customed matrix, but also induces random variables for random acceleration to update the step length, which overcomes the inflexibility of the old al-gorithms' fixed step length. We prove the global convergence of the new algorithm under certain mild conditions. And preliminary numerical experiments show that the algorithm is effective and the gPADMM converges faster than the old algorithms.

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