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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 3; pp. 1847 - 1854
Main Authors: Wu, Xuyang, Wang, He, Lu, Jie
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:0018-9286, 1558-2523, 1558-2523
Online Access:Get full text
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Summary: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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ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2022.3169955