Distributed proximal-gradient methods for convex optimization with inequality constraints

We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penal...

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Main Authors: Li, J., Wu, Changzhi, Wu, Z., Long, Q., Wang, Xiangyu
Format: Journal Article
Published: Australian Mathematical Society 2014
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/41558
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author Li, J.
Wu, Changzhi
Wu, Z.
Long, Q.
Wang, Xiangyu
author_facet Li, J.
Wu, Changzhi
Wu, Z.
Long, Q.
Wang, Xiangyu
author_sort Li, J.
building Curtin Institutional Repository
collection Online Access
description We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penalty function method. Our transformed problem has a smaller number of variables and a simpler structure than the existing distributed primal–dual subgradient methods for constrained distributed optimization problems. Using the special structure of this problem, we then propose a distributed proximal-gradient algorithm over a time-changing connectivity network, and establish a convergence rate depending on the number of iterations, the network topology and the number of agents. Although the transformed problem is nonsmooth by nature, our method can still achieve a convergence rate, O(1/k) , after k iterations, which is faster than the rate, O(1/ sqrt k), of existing distributed subgradient-based methods. Simulation experiments on a distributed state estimation problem illustrate the excellent performance of our proposed method.
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institution Curtin University Malaysia
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spelling curtin-20.500.11937-415582017-09-13T14:15:44Z Distributed proximal-gradient methods for convex optimization with inequality constraints Li, J. Wu, Changzhi Wu, Z. Long, Q. Wang, Xiangyu proximal-gradient method convex optimization exact penalty function method distributed algorithm We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penalty function method. Our transformed problem has a smaller number of variables and a simpler structure than the existing distributed primal–dual subgradient methods for constrained distributed optimization problems. Using the special structure of this problem, we then propose a distributed proximal-gradient algorithm over a time-changing connectivity network, and establish a convergence rate depending on the number of iterations, the network topology and the number of agents. Although the transformed problem is nonsmooth by nature, our method can still achieve a convergence rate, O(1/k) , after k iterations, which is faster than the rate, O(1/ sqrt k), of existing distributed subgradient-based methods. Simulation experiments on a distributed state estimation problem illustrate the excellent performance of our proposed method. 2014 Journal Article http://hdl.handle.net/20.500.11937/41558 10.1017/S1446181114000273 Australian Mathematical Society restricted
spellingShingle proximal-gradient method
convex optimization
exact penalty function method
distributed algorithm
Li, J.
Wu, Changzhi
Wu, Z.
Long, Q.
Wang, Xiangyu
Distributed proximal-gradient methods for convex optimization with inequality constraints
title Distributed proximal-gradient methods for convex optimization with inequality constraints
title_full Distributed proximal-gradient methods for convex optimization with inequality constraints
title_fullStr Distributed proximal-gradient methods for convex optimization with inequality constraints
title_full_unstemmed Distributed proximal-gradient methods for convex optimization with inequality constraints
title_short Distributed proximal-gradient methods for convex optimization with inequality constraints
title_sort distributed proximal-gradient methods for convex optimization with inequality constraints
topic proximal-gradient method
convex optimization
exact penalty function method
distributed algorithm
url http://hdl.handle.net/20.500.11937/41558