Distributed Optimization With Coupling Constraints
In this article, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dua...
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| Veröffentlicht in: | IEEE transactions on automatic control Jg. 68; H. 3; S. 1847 - 1854 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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IEEE
01.03.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9286, 1558-2523, 1558-2523 |
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| Abstract | In this article, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dual, proximal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the problem over a connected, undirected graph. We show that IPLUX achieves an <inline-formula><tex-math notation="LaTeX">O(1/k)</tex-math></inline-formula> rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation. |
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| AbstractList | In this article, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dual, proximal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the problem over a connected, undirected graph. We show that IPLUX achieves an <inline-formula><tex-math notation="LaTeX">O(1/k)</tex-math></inline-formula> rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation. In this paper, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dual, proximal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the problem over a connected, undirected graph. We show that IPLUX achieves an <formula><tex>$O(1/k)$</tex></formula> rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation. In this article, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dual, proximal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the problem over a connected, undirected graph. We show that IPLUX achieves an [Formula Omitted] rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation. |
| Author | Lu, Jie Wu, Xuyang Wang, He |
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| Cites_doi | 10.1137/090770102 10.1016/j.automatica.2017.07.003 10.1109/TAC.2022.3169955 10.1016/j.automatica.2020.108962 10.1109/TAC.2014.2308612 10.1137/16M1059011 10.1561/2200000016 10.1109/TAC.2014.2364096 10.1109/TIE.2016.2617832 10.1109/TAC.2020.2989282 10.1109/TCNS.2019.2925267 10.1109/TCYB.2019.2933003 10.1109/TAC.2019.2912494 10.1109/TSP.2015.2461520 10.1109/CDC42340.2020.9303937 10.1016/j.automatica.2013.01.009 10.1109/TSP.2016.2544743 10.1109/CDC.2018.8619322 |
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| SubjectTerms | Algorithms Computational geometry Constrained optimization Convergence Convex functions Convex optimisation Convex optimization Convexity Coupling Coupling constraints Couplings Distributed algorithms Distributed optimization Feasibility Inequality constraint Linear programming Mathematical transformations Optimisations Optimization primal-dual method Primal-dual methods proximal algorithm Transforms Undirected graphs Virtual addresses |
| Title | Distributed Optimization With Coupling Constraints |
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