Regularized Primal-Dual Subgradient Method for Distributed Constrained Optimization

In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized pr...

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Vydáno v:IEEE transactions on cybernetics Ročník 46; číslo 9; s. 2109 - 2118
Hlavní autoři: Deming Yuan, Ho, Daniel W. C., Shengyuan Xu
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.09.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Average consensus
constrained optimization
Convergence
Convex functions
Cost function
Cybernetics
distributed optimization
Lagrangian functions
Linear programming
primal–dual subgradient method
ISSN:2168-2267, 2168-2275
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Shrnutí:In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an O(K -1/4 ) convergence rate for general distributed constrained optimization, where K is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.
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ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2015.2464255