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...
| Main Authors: | , , , , , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/57713 |
| _version_ | 1848760077453885440 |
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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. |
| first_indexed | 2025-11-14T10:10:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-57713 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:10:03Z |
| publishDate | 2017 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |