Constrained And Robust Dynamic Optimization Algorithms Over Distributed Multi-Agent Networks

There are many fileds that need to apply optimization algorithms to solve optimiza-tion problems,such as machine learning,source allocation,data mining,auto-control,atc.With the development of technology of big data,cloud computing,5G commu-nication and IoT,the research of distributed optimization algorithm is paid more and more attention.Distributed optimization is that multi-agent cooperatively solve the op-timization problem over a network.Compared to centralized optimization,distributed optimization is more flexible and more extensible,has higher computing power and big-ger storage space.Distributed optimization can divided into centralized distributed opti-mization and decentralized distributed optimization,this thesis focus on distributed con-strained optimization over centralized network and robust dynamic optimization over decentralized network.In a centralized network,we consider a distributed constrained optimisation prob-lem where a group of distributed agents are interconnected via a cloud center,and col-laboratively minimise a network-wide objective function subject to local and global constraints.This thesis devotes to developing efficient distributed algorithms that fully utilise the computation abilities of the cloud center and the agents,as well as avoid ex-tensive communications between the cloud center and the agents.We address these is-sues by introducing two divide-and-conquer techniques,the alternating direction method of multipliers(ADMM)and a primal-dual first-order(PDFO)method,which assign the local objective functions and constraints to the agents while the global ones to the cloud center.Both algorithms are proved to be convergent to the primal-dual optimal solu-tion.Numerical experiments demonstrate the effectiveness of the proposed distributed constrained optimisation algorithms.In a decentralized network,we consider the problem of tracking a network-wide solution that dynamically minimizes the summation of time-varying local cost functions of network agents,when some of the agents are malfunctioning.The malfunctioning agents broadcast faulty values to their neighbors,and lead the optimization process to a wrong direction.To mitigate the influence of the malfunctioning agents,we propose a total variation(TV)norm regularized formulation that drives the local variables of the regular agents to be close,while allows them to be different with the faulty values broadcast by the malfunctioning agents.We give a sufficient condition under which consensus of the regular agents is guaranteed,and bound the gap between the consen-sual solution and the optimal solution we pursue as if the malfunctioning agents do not exist A fully decentralized subgradient algorithm is proposed to solve the TV norm reg-ularized problem in a dynamic manner.At every time,every regular agent only needs one subgradient evaluation of its current local cost function,in addition to combining messages received from neighboring regular and malfunctioning agents.The tracking error is proved to be bounded,given that variation of the optimal solution is bounded.Numerical experiments demonstrate the robust tracking performance of the proposed algorithm at presence of the malfunctioning agents.