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Primal-Dual Methods for Large-Scale and Distributed Convex Optimization and Data Analytics
Proceedings of the IEEE ( IF 20.6 ) Pub Date : 2020-11-01 , DOI: 10.1109/jproc.2020.3007395
Dusan Jakovetic , Dragana Bajovic , Joao Xavier , Jose M. F. Moura

The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given “difficult” (constrained) problem via finding solutions of a sequence of “easier” (often unconstrained) subproblems with respect to the original (primal) variable, wherein constraints satisfaction is controlled via the so-called dual variables. ALM is highly flexible with respect to how primal subproblems can be solved, giving rise to a plethora of different primal–dual methods. The powerful ALM mechanism has recently proved to be very successful in various large-scale and distributed applications. In addition, several significant advances have appeared, primarily on precise complexity results with respect to computational and communication costs in the presence of inexact updates and design and analysis of novel optimal methods for distributed consensus optimization. We provide a tutorial-style introduction to ALM and its variants for solving convex optimization problems in large-scale and distributed settings. We describe control-theoretic tools for the algorithms’ analysis and design, survey recent results, and provide novel insights into the context of two emerging applications: federated learning and distributed energy trading.

中文翻译:

用于大规模分布式凸优化和数据分析的原始对偶方法

增广拉格朗日方法 (ALM) 是一种经典的优化工具,它通过寻找相对于原始(原始)变量的一系列“更简单”(通常是无约束)子问题的解来解决给定的“困难”(约束)问题,其中约束满意度是通过所谓的双重变量来控制的。ALM 在如何解决原始子问题方面非常灵活,从而产生了大量不同的原始对偶方法。强大的 ALM 机制最近被证明在各种大规模和分布式应用程序中非常成功。此外,还出现了几项重大进展,主要是在存在不精确更新的情况下计算和通信成本方面的精确复杂性结果以及分布式共识优化的新型优化方法的设计和分析。我们提供了 ALM 及其变体的教程式介绍,用于解决大规模和分布式设置中的凸优化问题。我们描述了用于算法分析和设计的控制理论工具,调查了最近的结果,并对两个新兴应用的背景提供了新的见解:联邦学习和分布式能源交易。
更新日期:2020-11-01
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