On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation

Abstract

We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. The values of each function are assumed to reside at a different memory element. A single processing element is designated to approximate the value of the maximum of the sum of these functions by adopting a certain protocol. Under certain assumptions on the class of permissible protocols, we obtain the minimum number of real-valued messages that has to be transferred between the processing element and the memory elements in order to find the desired approximation of this maximum. In particular, we exploit the optimality of the nonadaptive protocols for the Lipschitzian optimization problem, studied in the context of information-based complexity, to prove our main result.