Gradient-free distributed optimization with exact convergence

In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called pseudo-gradient to guide the updates of the decision variables, which can...

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Main Authors: Pang, Yipeng, Hu, Guoqiang
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/163543
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1635432022-12-08T08:48:03Z Gradient-free distributed optimization with exact convergence Pang, Yipeng Hu, Guoqiang School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Distributed Optimization Gradient-Free Methods In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called pseudo-gradient to guide the updates of the decision variables, which can be applied in the fields where the gradient information is unknown, not available or non-existent. A surplus-based method is adopted to remove the doubly stochastic requirement on the weighting matrix, which enables the implementation of the algorithm in graphs having no associated doubly stochastic weighting matrix. For the convergence results, the proposed algorithm is able to obtain the exact convergence to the optimal value with any positive, non-summable and non-increasing step-sizes. Furthermore, when the step-size is also square-summable, the proposed algorithm is guaranteed to achieve the exact convergence to an optimal solution. In addition to the standard convergence analysis, the convergence rate of the proposed algorithm is also investigated. Finally, the effectiveness of the proposed algorithm is verified through numerical simulations. Ministry of Education (MOE) This work was supported by Singapore Ministry of Education Academic Research Fund Tier 1 RG180/17 (2017-T1-002-158). 2022-12-08T08:48:03Z 2022-12-08T08:48:03Z 2022 Journal Article Pang, Y. & Hu, G. (2022). Gradient-free distributed optimization with exact convergence. Automatica, 144, 110474-. https://dx.doi.org/10.1016/j.automatica.2022.110474 0005-1098 https://hdl.handle.net/10356/163543 10.1016/j.automatica.2022.110474 2-s2.0-85134325948 144 110474 en RG180/17 2017-T1-002-158 Automatica © 2022 Elsevier Ltd. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Distributed Optimization
Gradient-Free Methods
spellingShingle Engineering::Electrical and electronic engineering
Distributed Optimization
Gradient-Free Methods
Pang, Yipeng
Hu, Guoqiang
Gradient-free distributed optimization with exact convergence
description In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called pseudo-gradient to guide the updates of the decision variables, which can be applied in the fields where the gradient information is unknown, not available or non-existent. A surplus-based method is adopted to remove the doubly stochastic requirement on the weighting matrix, which enables the implementation of the algorithm in graphs having no associated doubly stochastic weighting matrix. For the convergence results, the proposed algorithm is able to obtain the exact convergence to the optimal value with any positive, non-summable and non-increasing step-sizes. Furthermore, when the step-size is also square-summable, the proposed algorithm is guaranteed to achieve the exact convergence to an optimal solution. In addition to the standard convergence analysis, the convergence rate of the proposed algorithm is also investigated. Finally, the effectiveness of the proposed algorithm is verified through numerical simulations.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Pang, Yipeng
Hu, Guoqiang
format Article
author Pang, Yipeng
Hu, Guoqiang
author_sort Pang, Yipeng
title Gradient-free distributed optimization with exact convergence
title_short Gradient-free distributed optimization with exact convergence
title_full Gradient-free distributed optimization with exact convergence
title_fullStr Gradient-free distributed optimization with exact convergence
title_full_unstemmed Gradient-free distributed optimization with exact convergence
title_sort gradient-free distributed optimization with exact convergence
publishDate 2022
url https://hdl.handle.net/10356/163543
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