论文标题
用于集中和分布式优化的完全平行的原始二重式算法
A Fully Parallel Primal-Dual Algorithm for Centralized and Distributed Optimization
论文作者
论文摘要
在本文中，考虑了基于单调操作员分裂方法得出具有固定步长的完全平行的二离散时间算法的集中式两块可分离优化。在此算法中，原始变量以交替的方式进行更新，例如乘数的交替方向方法（ADMM）。但是，与现有的离散时间算法（例如乘数方法（MM），ADMM，双向方向方法（BIADMM）（BIADMM）和原始偶型固定点（PDFP）算法不同，所有这些算法都遭受了依次更新，所有原始和二变量都可以在每次更新的含义上更新，从而在每个变量上都更新了，该变量是在更新的情况下更新的。该算法的优点之一是，其直接扩展到多块优化仍然是收敛的。然后将该方法应用于分布式优化，为此获得了完全并行的双偶分布式算法。最后，由于ADMM的直接扩展可能会以多块优化的形式差异，因此给出了三块块优化的数值示例，其中显示了所提出的算法的直接扩展可将其收敛到解决方案。
In this paper, a centralized two-block separable optimization is considered for which a fully parallel primal-dual discrete-time algorithm with fixed step size is derived based on monotone operator splitting method. In this algorithm, the primal variables are updated in an alternating fashion like Alternating Direction Method of Multipliers (ADMM). However, unlike existing discrete-time algorithms such as Method of Multipliers (MM), ADMM, Bi-Alternating Direction Method of Multipliers (BiADMM), and Primal-Dual Fixed Point (PDFP) algorithms, that all suffer from sequential updates, all primal and dual variables are updated in parallel in the sense that to update a variable at each time, updated version of other variable(s) is not required. One of advantages of the proposed algorithm is that its direct extension to multi-block optimization is still convergent. Then the method is applied to distributed optimization for which a fully parallel primal-dual distributed algorithm is obtained. Finally, since direct extension of ADMM may diverge for multi-block optimization, a numerical example of a three-block optimization is given for which the direct extension of the proposed algorithm is shown to converge to a solution.
