多个体网络分布式随机投影无梯度优化算法

Distributed Random Projection Gradient-Free Optimization Algorithm for MultiAgent Networks

研究了有向多个体网络的无梯度优化问题,提出了一种分布式随机投影无梯度优化算法。假定网络的优化目标函数可分解成所有个体的目标函数之和,每个个体仅知其自身的目标函数及其自身的状态约束集。运用无梯度方法解决了因个体目标函数可能非凸而引起的次梯度无法计算问题,并结合随机投影算法解决了约束集未知或约束集投影运算受限的问题。在该算法作用下,所有个体状态几乎必然收敛到优化集内,并且网络目标函数得到最优。

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 objectivefunction maybe nonconvex, the problem that the subgradient of each agent’s objective function hard to be calculatedcan be solved by using the gradient method. Then applying the random projection algorithm at each iteration, theproblem of the constrained set maybe unknown or the projection of the constrained set hard to be computed can alsobe solved. It is proved that, under the proposed algorithm, all agents’states converge to the optimization set almostsurely and the objective function of the network also achieves optimization.