Globally-Constrained Decentralized Optimization with Variable Coupling

Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet. Motivated by this, we study a class of globally-constrained...

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Bibliographic Details
Published in:IEEE transactions on automatic control pp. 1 - 14
Main Authors: Wang, Dandan, Wu, Xuyang, Ou, Zichong, Lu, Jie
Format: Journal Article
Language:English
Published: IEEE 2025
Subjects:
Convergence
Convex functions
Couplings
Decentralized optimization
Decision feedback equalizers
globally-coupled constraint
Information science
Linear programming
Nickel
Optimization
Optimization models
primal-dual algorithm
variable coupling
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet. Motivated by this, we study a class of globally-constrained decentralized optimization problems with a variable coupling structure that is new to the literature. Specifically, we consider a network of nodes collaborating to minimize a global objective subject to a collection of global inequality and equality constraints, which are formed by the local objective and constraint functions of the nodes. On top of that, we allow such local functions to depend on not only the corresponding node's decision variable but the decisions of its neighbors as well. To address this problem, we propose a decentralized projected primal-dual algorithm, which incorporates gradient projection and virtual-queue techniques with a primal-dual-primal scheme. Under mild conditions, we derive <inline-formula><tex-math notation="LaTeX">O(1/k)</tex-math></inline-formula> convergence rates for both objective error and constraint violations. Finally, two numerical experiments corroborate our theoretical results and illustrate the competitive performance of the proposed algorithm.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3629001