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    We introduce NGTAdam, a novel distributed optimization algorithm for large-scale networks. This method enhances convergence speed and performance in dynamic online optimization problems.

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    Area of Science:

    • Distributed Optimization
    • Networked Systems
    • Machine Learning Algorithms

    Background:

    • Online optimization problems over large-scale networks present significant computational challenges.
    • Adapting to dynamic changes and achieving fast convergence are critical for practical applications.

    Purpose of the Study:

    • To develop an accelerated distributed optimization algorithm for online problems.
    • To design an algorithm that balances fast convergence with robust performance in dynamic environments.

    Main Methods:

    • Proposed a novel algorithm, NGTAdam, combining Nesterov acceleration and adaptive moment estimation.
    • Analyzed convergence using linear system inequality to evaluate dynamic regret.
    • Derived an upper bound on dynamic regret dependent on initial conditions and problem dynamics.

    Main Results:

    • NGTAdam demonstrates effective adaptation to dynamic changes.
    • The algorithm achieves a fast convergence rate while maintaining good performance.
    • Numerical experiments confirm NGTAdam outperforms existing state-of-the-art distributed online optimization algorithms.

    Conclusions:

    • NGTAdam offers a superior approach for distributed online optimization in large-scale networks.
    • The algorithm's dynamic regret is sublinear under specific time-varying conditions.
    • This work advances the field of accelerated distributed optimization for dynamic systems.