Distributed Online Convex Optimization Over Time-Varying Unbalanced Digraphs With Multiple Coupled Constraints

This article aims to solve the distributed online convex optimization (DOCO) problems subjected to multiple coupled constraints over time-varying (TV) unbalanced digraphs. The existing global constraint models and coupled constraint models, where the number of constraints is related to the number of nodes, are not sufficient to reflect the characteristics of multiple coupled constrained optimization problems. On account of this drawback, a multiple coupled constraint model is constructed, which contains several coupled constraints, only including a part of all nodes. In addition, practical TV scenarios commonly come with complex network connectivity, which requires diverse matrices for fusing various information. In view of connectivity requirements, a novel TV distributed primal–dual push–pull (TDPP) algorithm, which can convert two types of weight matrices to all onefold row stochastic (RS) matrices, is proposed to tackle multiple coupled constrained problems. Under some general and necessary assumptions and conditions, both desired sublinear dynamic regret and constraint violation can be acquired by a strict theoretical analysis. Finally, two numerical examples are utilized to verify the superiority and validity of the TDPP algorithm compared with similar algorithms.