Distributed nonconvex constrained optimization over time-varying digraphs

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-...

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Published in:	Mathematical programming Vol. 176; no. 1-2; pp. 497 - 544
Main Authors:	Scutari, Gesualdo, Sun, Ying
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019 Springer Nature B.V
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Economic models Engineering education Full Length Paper Graph theory Machine learning Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear programming Numerical Analysis Optimization Theoretical 90C90 65K10 91A10 65K15 49M27 90C33
ISSN:	0025-5610, 1436-4646
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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.
AbstractList	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.
Author	Scutari, Gesualdo Sun, Ying
Author_xml	– sequence: 1 givenname: Gesualdo orcidid: 0000-0002-6453-6870 surname: Scutari fullname: Scutari, Gesualdo email: gscutari@purdue.edu organization: School of Industrial Engineering, Purdue University – sequence: 2 givenname: Ying surname: Sun fullname: Sun, Ying organization: School of Industrial Engineering, Purdue University
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Snippet	This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first...
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SubjectTerms	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Convergence Economic models Engineering education Full Length Paper Graph theory Machine learning Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear programming Numerical Analysis Optimization Theoretical
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Title	Distributed nonconvex constrained optimization over time-varying digraphs
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