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Distributed nonconvex constrained optimization over time-varying digraphs

  • Gesualdo ScutariEmail author
  • Ying Sun
Full Length Paper Series B
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Abstract

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) function—the agent’s sum-utility—plus 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.

Mathematics Subject Classification

90C33 90C90 91A10 49M27 65K15 65K10 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.School of Industrial EngineeringPurdue UniversityWest LafayetteUSA

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