Distributed nonconvex constrained optimization over time-varying digraphs
成果类型：
Article; Proceedings Paper
署名作者：
Scutari, Gesualdo; Sun, Ying
署名单位：
Purdue University System; Purdue University
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-018-01357-w
发表日期：
2019
页码：
497-544
关键词：
摘要：
This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex (nonseparable) functionthe agent's sum-utilityplus a difference-of-convex function (with nonsmooth convex part). This general formulation arises in many applications, from statistical machine learning to engineering. The proposed distributed method combines successive convex approximation techniques with a judiciously designed perturbed push-sum consensus mechanism that aims to track locally the gradient of the (smooth part of the) sum-utility. Sublinear convergence rate is proved when a fixed step-size (possibly different among the agents) is employed whereas asymptotic convergence to stationary solutions is proved using a diminishing step-size. Numerical results show that our algorithms compare favorably with current schemes on both convex and nonconvex problems.
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