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    Area of Science:

    • Optimization Theory
    • Distributed Systems
    • Network Engineering

    Background:

    • Resource allocation is crucial in distributed systems.
    • Nonsmooth cost functions and heterogeneous constraints pose significant challenges.
    • Existing methods often struggle with complex network and local constraints.

    Purpose of the Study:

    • To develop a distributed algorithm for optimal resource allocation.
    • To address nonsmooth cost functions and heterogeneous constraints.
    • To analyze the convergence properties of the proposed algorithm.

    Main Methods:

    • A distributed subgradient-based algorithm was designed.
    • Convergence analysis was performed for various network structures (digraphs, undirected graphs) and cost function types (strongly convex, strictly convex).
    • The algorithm was tested using simulation examples.

    Main Results:

    • The algorithm achieves optimal resource allocation under specified conditions.
    • Guaranteed convergence to the optimal solution for agents.
    • Effectiveness demonstrated across different network topologies and cost functions.

    Conclusions:

    • The proposed distributed subgradient algorithm effectively solves complex resource allocation problems.
    • The algorithm offers a robust solution for systems with nonsmooth costs and heterogeneous constraints.
    • Validated convergence ensures reliable optimal resource distribution in networked systems.