A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909132879036416 |
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| author | Ou, Zichong Qiu, Chenyang Wang, Dandan Lu, Jie |
| author_facet | Ou, Zichong Qiu, Chenyang Wang, Dandan Lu, Jie |
| contents | In this paper, we develop a distributed mixing-accelerated primal-dual proximal algorithm, referred to as MAP-Pro, which enables nodes in multi-agent networks to cooperatively minimize the sum of their nonconvex, smooth local cost functions in a decentralized fashion. The proposed algorithm is constructed upon minimizing a computationally inexpensive augmented-Lagrangian-like function and incorporating a time-varying mixing polynomial to expedite information fusion across the network. The convergence results derived for MAP-Pro include a sublinear rate of convergence to a stationary solution and, under the Polyak-Łojasiewics (P-Ł) condition, a linear rate of convergence to the global optimal solution. Additionally, we may embed the well-noted Chebyshev acceleration scheme in MAP-Pro, which generates a specific sequence of mixing polynomials with given degrees and enhances the convergence performance based on MAP-Pro. Finally, we illustrate the competitive convergence speed and communication efficiency of MAP-Pro via a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02830 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization Ou, Zichong Qiu, Chenyang Wang, Dandan Lu, Jie Optimization and Control Systems and Control In this paper, we develop a distributed mixing-accelerated primal-dual proximal algorithm, referred to as MAP-Pro, which enables nodes in multi-agent networks to cooperatively minimize the sum of their nonconvex, smooth local cost functions in a decentralized fashion. The proposed algorithm is constructed upon minimizing a computationally inexpensive augmented-Lagrangian-like function and incorporating a time-varying mixing polynomial to expedite information fusion across the network. The convergence results derived for MAP-Pro include a sublinear rate of convergence to a stationary solution and, under the Polyak-Łojasiewics (P-Ł) condition, a linear rate of convergence to the global optimal solution. Additionally, we may embed the well-noted Chebyshev acceleration scheme in MAP-Pro, which generates a specific sequence of mixing polynomials with given degrees and enhances the convergence performance based on MAP-Pro. Finally, we illustrate the competitive convergence speed and communication efficiency of MAP-Pro via a numerical example. |
| title | A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2304.02830 |