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    This study introduces a distributed algorithm for solving mixed equilibrium problems (EP) across multiple sets. The method ensures agents cooperatively find a solution, demonstrating effectiveness in simulations.

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    Area of Science:

    • Optimization Theory
    • Distributed Systems
    • Convex Analysis

    Background:

    • Investigates the challenge of distributively solving mixed equilibrium problems (EP) involving multiple convex sets.
    • Addresses scenarios where agents have limited access to local bifunctions and convex sets.

    Purpose of the Study:

    • To develop a distributed algorithm for cooperative agents to find a solution in the intersection of multiple convex sets.
    • To ensure the sum of multiple bifunctions with a free variable is nonnegative within the network.

    Main Methods:

    • Proposes a novel distributed algorithm combining mirror descent, primal-dual, and consensus algorithms with a fixed step size.
    • Agents utilize local information from their own bifunction and convex set.

    Main Results:

    • Proves asymptotic convergence of all agents' states to a solution of the mixed EP under mild conditions.
    • Demonstrates the algorithm's effectiveness through a numerical simulation example.

    Conclusions:

    • The proposed distributed algorithm is effective for solving mixed equilibrium problems in decentralized networks.
    • Theoretical results are validated by practical simulation, showing convergence to a valid solution.