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Gradient‐free method for distributed multi‐agent optimization via push‐sum algorithms
Author(s) -
Yuan Deming,
Xu Shengyuan,
Lu Junwei
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3164
Subject(s) - convergence (economics) , convex function , sequence (biology) , mathematical optimization , function (biology) , computer science , frank–wolfe algorithm , rate of convergence , matrix (chemical analysis) , algorithm , variable (mathematics) , convex optimization , mathematics , regular polygon , convex set , computer network , mathematical analysis , channel (broadcasting) , materials science , geometry , evolutionary biology , biology , economics , composite material , genetics , economic growth
Summary This paper studies the problem of minimizing the sum of convex functions that all share a common global variable, each function is known by one specific agent in the network. The underlying network topology is modeled as a time‐varying sequence of directed graphs, each of which is endowed with a non‐doubly stochastic matrix. We present a distributed method that employs gradient‐free oracles and push‐sum algorithms for solving this optimization problem. We establish the convergence by showing that the method converges to an approximate solution at the expected rate of O ( ln T / T) , where T is the iteration counter. A numerical example is also given to illustrate the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.