Asynchronous Optimization Over Graphs: Linear Convergence Under Error Bound Conditions

We consider convex and nonconvex constrained optimization with a partially separable objective function: Agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables of that agent and those of a few others. This partitioned se...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 66; no. 10; pp. 4604 - 4619
Main Authors: Cannelli, Loris, Facchinei, Francisco, Scutari, Gesualdo, Kungurtsev, Vyacheslav
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asynchronous algorithms
Convergence
Convexity
Delays
error bounds
Indexes
Linear programming
linear rate
multiagent systems
Nickel
nonconvex optimization
Optimization
Partitioning algorithms
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:We consider convex and nonconvex constrained optimization with a partially separable objective function: Agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables of that agent and those of a few others. This partitioned setting arises in several applications of practical interest. We propose what is, to the best of our knowledge, the first distributed, asynchronous algorithm with rate guarantees for this class of problems. When the objective function is nonconvex, the algorithm provably converges to a stationary solution at a sublinear rate whereas linear rate is achieved under the renowned Luo-Tseng error bound condition (which is less stringent than strong convexity). Numerical results on matrix completion and LASSO problems show the effectiveness of our method.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3033490