  This paper considers computation offloading in fog-radio access networks
(F-RAN), where multiple user equipments (UEs) offload their computation tasks
to the F-RAN through a number of fog nodes. Each UE can choose one of the fog
nodes to offload its task, and each fog node may serve multiple UEs. Depending
on the computation burden at the fog nodes, the tasks may be computed by the
fog nodes or further offloaded to the cloud via capacity-limited fronthaul
links. To compute all UEs' tasks as fast as possible, joint optimization of
UE-Fog association, radio and computation resources of F-RAN is proposed to
minimize the maximum latency of all UEs. This min-max problem is formulated as
a mixed integer nonlinear program (MINP). We first show that the MINP can be
reformulated as a continuous optimization problem, and then employ the
majorization minimization (MM) approach to find a solution. The MM approach
that we develop is unconventional in that -- each MM subproblem can be solved
inexactly with the same provable convergence guarantee as the conventional
exact MM, thereby reducing the complexity of each MM iteration. In addition, we
also consider a cooperative offloading model, where the fog nodes
compress-and-forward their received signals to the cloud. Under this model, a
similar min-max latency optimization problem is formulated and tackled again by
the inexact MM approach. Simulation results show that the proposed algorithms
outperform some heuristic offloading strategies, and that the cooperative
offloading can better exploit the transmission diversity to attain better
latency performance than the non-cooperative one.
