A Zero-Order Improved Algorithm Based On Push-Sum Algorithm For Distributed Convex Optimization

In recent years,the problem of distributed optimization of multi-agent networks has attracted the attention of many scholars.Distributed convex optimization is one of the most important research topics.At present,subgradient algorithm for distributed convex optimization is mostly used.However,in many practical situations,the subgradient of the problem is often difficult to calculate,sometimes is even unavailable.Therefore,a zero-order algorithm for distributed convex optimization is researched in this paper.Firstly,the non-smooth function is approximated by the Gaussian smoothing method.Second-ly,the Push-Sum protocol is used to consider the distributed Gradient-Free algorithm in time-varying directed networks.Then,based on this algorithm,the communication noise between multi-agents is considered to solve the distributed convex problem and the distributed strongly convex problem.More importantly,the obvious convergence result is proved.The main contents include the following three aspects:1.Firstly,a Gradient-Free algorithm based on Push-Sum protocol for distributed strongly convex optimization over time-varying directed network topology is proposed.The convergence of the algorithm is analyzed,and more importantly,the convergence rate of the algorithm is obtained as O(ln ?/?).Finally,numerical experiments show that the proposed algorithm has similar convergence with the corresponding sub-gradient algorithm.2.Secondly,a Gradient-Free algorithm with random communication noise based on Push-Sum protocol for distributed convex optimization over time-varying directed net-work topology is proposed.The convergence analysis of the algorithm is given.When each local objective function is a convex function,the convergence rate of the algorithm DFPS-N is 0(lnt/(?)).numerical experiments show that the algorithm has good conver-gence.3.Finally,the Gradient-Free algorithm with random communication noise based on Push-Sum protocol over time-varying directed network topology to solve distributed strongly convex optimization,that is,when each local objective function fi is a strong convex function.We get a convergence rate of O(lnt/t),which obviously converges faster than the convergence rate 0(lnt/(?))for general convex problems.