关键词: 多个体网络, 随机投影, 无梯度算法, 分布式优化

Abstract: This paper proposes a distributed random projection gradient-free optimization algorithm for multi-agent networks. It is assumed that the objective function of the network is the sum of the objective functions of all individuals, and each individual only knows its own objective function and its own state constraint set. Due to each agent’s objective function maybe nonconvex, the problem that the subgradient of each agent’s objective function hard to be calculated can be solved by using the gradient method. Then applying the random projection algorithm at each iteration, the problem of the constrained set maybe unknown or the projection of the constrained set hard to be computed can also be solved. It is proved that, under the proposed algorithm, all agents’ states converge to the optimization set almost surely and the objective function of the network also achieves optimization.

Key words: multi-agent network, random projection, gradient-free algorithm, distributed optimization