A distributed optimization method to resource allocation problem on directed communication network under time delays

This work solves the resource allocation problem (RAP) for the multi-agents on time-varying directed communication networks under time delays. When the total demand of the resources is an equality constraint, the demand of resources is allocated and each agent is limited to an inequality constraint which is usually named the state constraint. In practical, time delays have a great influence on RAP. Hence, we attend to solve this problem by a fully distributed optimization method. The RAP that is subject to the state constraints could be solved by introducing a stochastic gradient-push to store the residue at each step on each agent with state constraint. It is also has been proved that the our method converges globally when the time-varying directed communication network is jointly strongly connected. The most distinguishing feature of our method is that its converges globally for the time-varying communication network even under time delays.