Incremental gradient-free method for nonsmooth distributed optimization

In this paper we consider the minimization of the sum of local convex component functions distributed over a multi-agent network. We first extend the Nesterov's random gradient-free method to the incremental setting. Then we propose the incremental gradient-free methods, including a cyclic orde...

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Main Authors: Li, J., Li, G., Wu, Z., Wu, Changzhi, Wang, X., Lee, J., Jung, K.
Format: Journal Article
Published: American Institute of Mathematical Sciences 2017
Online Access:http://hdl.handle.net/20.500.11937/57713
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author Li, J.
Li, G.
Wu, Z.
Wu, Changzhi
Wang, X.
Lee, J.
Jung, K.
author_facet Li, J.
Li, G.
Wu, Z.
Wu, Changzhi
Wang, X.
Lee, J.
Jung, K.
author_sort Li, J.
building Curtin Institutional Repository
collection Online Access
description In this paper we consider the minimization of the sum of local convex component functions distributed over a multi-agent network. We first extend the Nesterov's random gradient-free method to the incremental setting. Then we propose the incremental gradient-free methods, including a cyclic order and a randomized order in the selection of component function. We provide the convergence and iteration complexity analysis of the proposed methods under some suitable stepsize rules. To illustrate our proposed methods, extensive numerical results on a distributed l 1 -regression problem are presented. Compared with existing incremental subgradient-based methods, our methods only require the evaluation of the function values rather than subgradients, which may be preferred by practical engineers.
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institution Curtin University Malaysia
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last_indexed 2025-11-14T10:10:03Z
publishDate 2017
publisher American Institute of Mathematical Sciences
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spelling curtin-20.500.11937-577132017-11-20T08:58:17Z Incremental gradient-free method for nonsmooth distributed optimization Li, J. Li, G. Wu, Z. Wu, Changzhi Wang, X. Lee, J. Jung, K. In this paper we consider the minimization of the sum of local convex component functions distributed over a multi-agent network. We first extend the Nesterov's random gradient-free method to the incremental setting. Then we propose the incremental gradient-free methods, including a cyclic order and a randomized order in the selection of component function. We provide the convergence and iteration complexity analysis of the proposed methods under some suitable stepsize rules. To illustrate our proposed methods, extensive numerical results on a distributed l 1 -regression problem are presented. Compared with existing incremental subgradient-based methods, our methods only require the evaluation of the function values rather than subgradients, which may be preferred by practical engineers. 2017 Journal Article http://hdl.handle.net/20.500.11937/57713 10.3934/jimo.2017021 American Institute of Mathematical Sciences unknown
spellingShingle Li, J.
Li, G.
Wu, Z.
Wu, Changzhi
Wang, X.
Lee, J.
Jung, K.
Incremental gradient-free method for nonsmooth distributed optimization
title Incremental gradient-free method for nonsmooth distributed optimization
title_full Incremental gradient-free method for nonsmooth distributed optimization
title_fullStr Incremental gradient-free method for nonsmooth distributed optimization
title_full_unstemmed Incremental gradient-free method for nonsmooth distributed optimization
title_short Incremental gradient-free method for nonsmooth distributed optimization
title_sort incremental gradient-free method for nonsmooth distributed optimization
url http://hdl.handle.net/20.500.11937/57713