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    This study introduces an event-triggered distributed stochastic mirror descent algorithm for resource-constrained multiagent optimization. The developed method ensures convergence, offering a sublinear upper bound with optimized communication costs.

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    Area of Science:

    • Distributed Optimization
    • Networked Multiagent Systems
    • Convex Optimization

    Background:

    • Bandwidth limitations in networked systems increase communication costs.
    • Efficient information exchange is crucial for distributed optimization.
    • Event-triggered strategies can reduce communication overhead.

    Purpose of the Study:

    • To address distributed convex constrained optimization in time-varying multiagent networks with bandwidth limitations.
    • To develop an efficient algorithm that minimizes communication costs using an event-triggered strategy.
    • To analyze the convergence properties of the proposed algorithm.

    Main Methods:

    • An event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm is proposed.
    • The algorithm utilizes Bregman divergence as a distance-measuring function.
    • Convergence analysis is performed to establish an upper bound dependent on the trigger threshold.

    Main Results:

    • The ET-DSMD algorithm is presented for multiagent optimization under convex constraints.
    • A sublinear convergence upper bound is guaranteed when the trigger threshold approaches zero.
    • The algorithm's feasibility is demonstrated through a distributed logistic regression example.

    Conclusions:

    • The ET-DSMD algorithm effectively handles distributed optimization in resource-constrained networks.
    • The event-triggered approach significantly reduces communication costs while ensuring convergence.
    • The study provides a practical solution for efficient multiagent optimization problems.