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Resource-aware Exact Decentralized Optimization Using Event-triggered Broadcasting

This work addresses the decentralized optimization problem where a group of agents with coupled private objective functions work together to exactly optimize the summation of local interests. Upon modeling the decentralized problem as an equality-constrained centralized one, we leverage the linearized augmented Lagrangian method (LALM) to design an event-triggered decentralized algorithm that only requires light local computation at generic time instants and peer-to-peer communication at sporadic triggering time instants. The triggering time instants for each agent are locally determined by comparing the deviation between true and broadcast primal variables with certain triggering thresholds. Provided that the threshold is summable over time, we established a new upper bound for the effect of triggering behavior on the primal-dual residual. Based on this, the same convergence rate $O(\frac{1}{k})$ with periodic algorithms is secured for nonsmooth convex problems. Stronger convergence results have been further established for strongly convex and smooth problems, that is, the iterates linearly converge with exponentially decaying triggering thresholds.} We examine the developed strategy in two common optimization problems; comparison results illustrate its performance and superiority in exploiting communication resources.