A Continuous-Time Algorithm for Distributed Optimization Based on Multiagent Networks

Abstract

Based on the multiagent networks, this paper introduces a continuous-time algorithm to deal with distributed convex optimization. Using nonsmooth analysis and algebraic graph theory, the distributed network algorithm is modeled by the aid of a nonautonomous differential inclusion, and each agent exchanges information from the first-order and the second-order neighbors. For any initial point, the solution of the proposed network can reach consensus to the set of minimizers if the graph has a spanning tree. In contrast to the existing continuous-time algorithms for distributed optimization, the proposed model holds the least number of state variables and relaxes the strongly connected weighted-balanced topology to the weaker case. The modified form of the proposed continuous-time algorithm is also given, and it is proven that this algorithm is suitable for solving distributed problems if the undirected network is connected. Finally, two numerical examples and an optimal placement problem confirm the effectiveness of the proposed continuous-time algorithm.