Distributed Multiagent Convex Optimization Over Random Digraphs

This paper considers an unconstrained collaborative optimization of a sum of convex functions, where agents make decisions using local information in the presence of random interconnection topologies. We recast the problem as minimization of the sum of convex functions over a constraint set defined...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 65; no. 3; pp. 986 - 998
Main Authors: Alaviani, Seyyed Shaho, Elia, Nicola
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asynchronous
Computational geometry
Convergence
Convex analysis
Convex functions
Convexity
distributed convex optimization
fixed-value point
Graph theory
Hilbert space
Mathematical analysis
Minimization
minimization over fixed-value point set
Multiagent systems
Operators (mathematics)
Optimization
Protocols
random graphs
Random variables
Topology
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This paper considers an unconstrained collaborative optimization of a sum of convex functions, where agents make decisions using local information in the presence of random interconnection topologies. We recast the problem as minimization of the sum of convex functions over a constraint set defined as the set of fixed-value points of a random operator derived from weighted matrices of random graphs. We show that the derived random operator has nonexpansivity property; therefore, this formulation does not need the distribution of random communication topologies. Hence, it includes random networks with/without asynchronous protocols. As an extension of the problem, we define a novel optimization problem, namely minimization of a convex function over the fixed-value point set of a nonexpansive random operator. We propose a discrete-time algorithm using diminishing step size for converging almost surely and in mean square to the global solution of the optimization problem under suitable assumptions. Consequently, as a special case, it reduces to a totally asynchronous algorithm for the distributed optimization problem. We show that fixed-value point is a bridge from deterministic analysis to random analysis of the algorithm. Finally, a numerical example illustrates the convergence of the proposed algorithm.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2937499