Gradient-free method for nonsmooth distributed optimization
In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network. We first extend the (centralized) Nesterov’s random gradient-free algorithm and Gaussian smoothing technique to the distributed case. Then, the convergence of the algorithm is proved. Fu...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Springer
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/35457 |
| _version_ | 1848754502139641856 |
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| author | Li, J. Wu, Changzhi Wu, Z. Long, Q. |
| author_facet | Li, J. Wu, Changzhi Wu, Z. Long, Q. |
| author_sort | Li, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network. We first extend the (centralized) Nesterov’s random gradient-free algorithm and Gaussian smoothing technique to the distributed case. Then, the convergence of the algorithm is proved. Furthermore, an explicit convergence rate is given in terms of the network size and topology. Our proposed method is free of gradient, which may be preferred by practical engineers. Since only the cost function value is required, our method may suffer a factor up to d (the dimension of the agent) in convergence rate over that of the distributed subgradient-based methods in theory. However, our numerical simulations show that for some nonsmooth problems, our method can even achieve better performance than that of subgradient-based methods, which may be caused by the slow convergence in the presence of subgradient. |
| first_indexed | 2025-11-14T08:41:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-35457 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:41:25Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-354572017-09-13T15:20:31Z Gradient-free method for nonsmooth distributed optimization Li, J. Wu, Changzhi Wu, Z. Long, Q. Convex optimization Distributed algorithm Gradient-free method Gaussian smoothing In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network. We first extend the (centralized) Nesterov’s random gradient-free algorithm and Gaussian smoothing technique to the distributed case. Then, the convergence of the algorithm is proved. Furthermore, an explicit convergence rate is given in terms of the network size and topology. Our proposed method is free of gradient, which may be preferred by practical engineers. Since only the cost function value is required, our method may suffer a factor up to d (the dimension of the agent) in convergence rate over that of the distributed subgradient-based methods in theory. However, our numerical simulations show that for some nonsmooth problems, our method can even achieve better performance than that of subgradient-based methods, which may be caused by the slow convergence in the presence of subgradient. 2015 Journal Article http://hdl.handle.net/20.500.11937/35457 10.1007/s10898-014-0174-2 Springer restricted |
| spellingShingle | Convex optimization Distributed algorithm Gradient-free method Gaussian smoothing Li, J. Wu, Changzhi Wu, Z. Long, Q. Gradient-free method for nonsmooth distributed optimization |
| title | Gradient-free method for nonsmooth distributed optimization |
| title_full | Gradient-free method for nonsmooth distributed optimization |
| title_fullStr | Gradient-free method for nonsmooth distributed optimization |
| title_full_unstemmed | Gradient-free method for nonsmooth distributed optimization |
| title_short | Gradient-free method for nonsmooth distributed optimization |
| title_sort | gradient-free method for nonsmooth distributed optimization |
| topic | Convex optimization Distributed algorithm Gradient-free method Gaussian smoothing |
| url | http://hdl.handle.net/20.500.11937/35457 |