Distributed accelerated proximal conjugate gradient methods for multi-agent constrained optimization problems

Abstract: The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M number of smooth and M number of nonsmooth functions over the common fixed points of M number of nonlinear mappings. Exploiting the special properties of the cost component function of the objective function and the nonlinear mapping of the constraint problem of each agent, a new inertial accelerated incremental and parallel computing distributed algorithms will be presented based on the combinations of computations of proximal, conjugate gradient and Halpern methods. Some numerical experiments and comparisons are given to illustrate our results.