Design of Distributed Optimization Algorithm Based on Unbalanced Directed Graph Communication Topology Diagram

The design of distributed optimization algorithms presents a multi-agent domain problem, offering advantages over traditional centralized optimization algorithms by requiring less information and leveraging faster information transmission, making it suitable for various application scenarios in modern production and life. However, while most distributed optimization algorithms are designed based on balanced graphs, practical projects often involve unbalanced directed graphs in their communication topology. To address this, the paper proposes a distributed discrete-time algorithm based on the row random matrix method and Lagrange multiplier method, tailored for distributed optimization problems with equality constraints and locally closed convex set constraints specifically for strongly connected fixed unbalanced directed graphs. This approach tackles challenges associated with the original row random matrix method's difficulty in handling equality constraints, requiring the introduction of a multiplication subsystem, while ensuring convergence speed.