Distributed convex optimization with coupling constraints over time-varying directed graphs^†

Abstract

This paper considers a distributed convex optimization problem over a timevarying multi-agent network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local constraints and global coupling constraints. Over directed graphs, we propose a distributed algorithm that incorporates the push-sum protocol into dual sub-gradient methods. Under the convexity assumption, the optimality of primal and dual variables, and the constraint violation are first established. Then the explicit convergence rates of the proposed algorithm are obtained. Finally, numerical experiments on the economic dispatch problem are provided to demonstrate the efficacy of the proposed algorithm.

Decentralized Convex Optimization Under Affine Constraints for Power Systems Control

“…Primarily motivated by the demand from the power systems community, various decentralized algorithms for coupled constraints have been proposed. Generally designed versatile for engineering applications, many of these algorithms assume restricted function domains Wang and Hu [2022], Liang et al [2019], Nedić et al [2018], Gong and Zhang [2023], Zhang et al [2021], Wu et al [2022], nonlinear inequality constraints Liang et al [2019], Gong and Zhang [2023], Wu et al [2022], time-varying graphs Zhang et al [2021], Nedić et al [2018] or utilize specific problem structure Wang and Hu [2022]. B ln 1 ε ) complexity bound, where B is the time the graph takes to reach connectivity.…”

A Privacy-Masking Learning Algorithm for Online Distributed Optimization over Time-Varying Unbalanced Digraphs

“…Compared with classical DO in which the local objective functions are usually time-invariant, online distributed optimization (ODO) is applicable to the circumstances where local objective functions possibly change over time in some uncertain and even adversarial environments. Various ODO approaches have been increasingly developed in recent years [3,4]. In [2], Schwartz initially gave a review on the advancement of online convex optimization.…”