Globally-Constrained Decentralized Optimization with Variable Coupling - Wang, Dandan; Wu, Xuyang; Ou, Zichong; Lu, Jie (IEEE transactions on automatic control, 2025)
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 O(1/k) 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.