Distributed Optimization Algorithms with Communications

We discuss the convergence properties of asynchro- at each time instance, on the adjustments of his decinous distributed iterative optimization algorithms, sions. So, in some sense, the synchronous model retolerating communication delays. We focus on a gra- quires "a lot of communications." dient-type algorithm for minimizing an additive cost (2) A second drawback of synchronous algorithms is that function and present sufficient conditions for conver- communication delays can introduce bottlenecks and slow gence. We view such an algorithm as a model of adjust- down the algorithm. In particular, the time between ment of the decisions of decision makers in an organiza- two consecutive updates has to be at least as large tion and we suggest that our results can be interpreted as the maximum communication delay between any pair of as guidelines for designing the information flows in decision makers. an organization. (3) Finally, complete synchronization is certainly an unrealistic model of human organizations.