Distributed Prediction-Correction ADMM for Time-Varying Convex Optimization
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913340327985152 |
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| author | Bastianello, Nicola Simonetto, Andrea Carli, Ruggero |
| author_facet | Bastianello, Nicola Simonetto, Andrea Carli, Ruggero |
| contents | This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on past observations, and exploit this information to solve the time-varying problem more effectively. In order to guarantee linear convergence of the algorithm, a regularization is applied to the dual, yielding a dual-regularized ADMM. We analyze the convergence properties of the time-varying algorithm, as well as the regularization error of the dual-regularized ADMM. Numerical results show that in time-varying settings, despite the regularization error, the performance of the dual-regularized ADMM can outperform inexact gradient-based methods, as well as exact dual decomposition techniques, in terms of asymptotical error and consensus constraint violation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2009_08335 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Distributed Prediction-Correction ADMM for Time-Varying Convex Optimization Bastianello, Nicola Simonetto, Andrea Carli, Ruggero Optimization and Control This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on past observations, and exploit this information to solve the time-varying problem more effectively. In order to guarantee linear convergence of the algorithm, a regularization is applied to the dual, yielding a dual-regularized ADMM. We analyze the convergence properties of the time-varying algorithm, as well as the regularization error of the dual-regularized ADMM. Numerical results show that in time-varying settings, despite the regularization error, the performance of the dual-regularized ADMM can outperform inexact gradient-based methods, as well as exact dual decomposition techniques, in terms of asymptotical error and consensus constraint violation. |
| title | Distributed Prediction-Correction ADMM for Time-Varying Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2009.08335 |