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    Area of Science:

    • Distributed optimization
    • Multiagent systems
    • Online learning

    Background:

    • Solving distributed constrained optimization problems in multiagent networks presents challenges due to time-varying objective functions and complex constraint sets.
    • Existing algorithms often require prior knowledge of the total number of iterations, limiting their applicability in dynamic online settings.

    Purpose of the Study:

    • To develop a novel consensus-based adaptive primal-dual subgradient algorithm for distributed constrained optimization.
    • To address time-varying objective functions and inequality constraints in a multiagent network setting.
    • To eliminate the need for advance knowledge of the total number of iterations.

    Main Methods:

    • Introduction of a regularized convex-concave function to facilitate the optimization process.
    • Development of a consensus-based adaptive primal-dual subgradient algorithm.
    • Analysis of regret bounds and constraint violation bounds.

    Main Results:

    • The proposed algorithm achieves a specified regret bound and a bound on constraint violation.
    • An improved regret bound is demonstrated when objective functions exhibit strong convexity.
    • The algorithm enables novel trade-offs between regret and constraint violation.

    Conclusions:

    • The developed algorithm effectively solves distributed constrained optimization problems in online settings.
    • It offers flexibility and improved performance compared to existing methods, particularly for strongly convex objectives.
    • Numerical examples confirm the algorithm's practical effectiveness.