  We provide a general framework for the problem of data offloading in a
heterogeneous wireless network, where some demand of cellular users is served
by a complementary network. The complementary network is either a small-cell
network that shares the same resources as the cellular network, or a WiFi
network that uses orthogonal resources. For a given demand served in a cellular
network, the load, or the level of resource usage, of each cell depends in a
non-linear manner on the load of other cells due to the mutual coupling of
interference seen by one another. With load coupling, we optimize the demand to
be served in the cellular or the complementary networks, so as to maximize a
utility function. We consider three representative utility functions that
balance, to varying degrees, the revenue from serving the users vs the user
fairness. We establish conditions for which the optimization problem has a
feasible solution and is convex, and hence tractable to numerical computations.
Finally, we propose a strategy with theoretical justification to constrain the
load to some maximum value, as required for practical implementation. Numerical
studies are conducted for both under-loaded and over-loaded networks.
