How do distributed optimization algorithms enable multi-agent systems to achieve global optimization goals while minimizing communication and computational overhead?

Distributed optimization algorithms enable multi-agent systems to achieve global optimization goals by allowing each agent to solve a local optimization problem while exchanging information with neighboring agents. This approach minimizes communication and computational overhead by:

1. Local Computation: Each agent computes its own local cost function and constraint, reducing the need for extensive communication and processing power.
2. Information Sharing: Agents share information about their local solutions with neighbors, facilitating convergence towards a global optimal solution.
3. Decentralization: The lack of a central controller reduces communication requirements and potential bottlenecks.
4. Efficient Algorithms: Algorithms like distributed subgradient and ADMM are designed to minimize communication and computation, ensuring efficient convergence.
5. Scalability: These algorithms can scale to large networks, making them suitable for complex multi-agent systems with numerous agents.