Distributed Convex Optimization on State-Dependent Undirected Graphs: Homogeneity Technique

This paper investigates the distributed convex optimization problem (DCOP) based on continuous-time multiagent systems under a state-dependent graph. The objective is to optimize the sum of local cost functions, each of which is only known by the corresponding agent. First, a piecewise continuous distributed optimization algorithm is proposed, such that all agents reach consensus in finite time and reach the optimal point of the total cost function asymptotically under a time-invariant graph. Then, another distributed optimization algorithm is presented to preserve the initial edges and make the agents solve DCOP on a state-dependent graph. In particular, any pair of agents can exchange information with each other when their geometry distance is less than a certain range. Finally, several simulations are given to verify the effectiveness of the proposed algorithms.