On the Convergence of Inexact Gradient Descent with Controlled Synchronization Steps

We develop a gradient-like algorithm to minimize sum of peer objective functions based on coordination through interconnection network. The admits two stages: the first is constitute gradient, possibly with errors, for updating locally replicated decision variables at each and second used error-free averaging synchronizing local replicas. Unlike many related algorithms, errors permitted in our can cover wide range inexactnesses, as long they are bounded. Moreover, we do not impose any gradient boundedness conditions functions. Furthermore, stage conducted periodic manner, like algorithms. Instead, verifiable criterion devised dynamically trigger peer-to-peer stage, so that expensive communication overhead significantly be reduced. Finally, convergence established under mild conditions.