Distributed optimization with hybrid linear constraints for multi-agent networks

This article investigates the distributed constrained optimization with hybrid linear constraints for multi-agent networks, in which all the agents collaboratively minimize the global objective function with a sum of convex local objective functions, while the constraints are more general with local and global restrictions on the agents. Based on matrix and graph theories, a discrete-time algorithm under distributed manner is designed to deal with the organized problems. In addition, the optimality of the presented algorithm is obtained under certain initial restriction for the agents. By virtue of a novel Lyapunov function and the optimal conditions, rigorous analysis shows the convergence of the multi-agent networks with undirected and connected graphs. Finally, two simulation examples are presented to validate the theoretical consequence.