ON THE DOUGLAS-RACHFORD SPLITTING METHOD AND THE PROXIMAL POINT ALGORITHM FOR MAXIMAL MONOTONE-OPERATORS
ON THE DOUGLAS-RACHFORD SPLITTING METHOD AND THE PROXIMAL POINT ALGORITHM FOR MAXIMAL MONOTONE-OPERATORS
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DOI：
10.1007/bf01581204
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发表时间：
1992-07-06
影响因子：
2.7
通讯作者：
BERTSEKAS, DP
中科院分区：
文献类型：
--
作者：
ECKSTEIN, J;BERTSEKAS, DP
本文通过一种称为分裂算子的算子表明，用于寻找两个单调算子之和的零点的道格拉斯 - 拉赫福德分裂方法是邻近点算法的一种特殊情况。因此，道格拉斯 - 拉赫福德分裂的应用，例如用于凸规划分解的交替方向乘子法，也是邻近点算法的特殊情况。这一观察结果使得各种凸规划算法能够统一和推广。通过引入邻近点算法的一个修正版本，我们推导出了一种新的、用于凸规划的广义交替方向乘子法。这类进展说明了将单调算子理论作为概念框架所获得的强大力量和通用性。
This paper shows, by means of an operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special cases of the proximal point algorithm. This observation allows the unification and generalization of a variety of convex programming algorithms. By introducing a modified version of the proximal point algorithm, we derive a new, generalized alternating direction method of multipliers for convex programming. Advances of this sort illustrate the power and generality gained by adopting monotone operator theory as a conceptual framework.