  We analyze the onset of inflation for a simple single-field model when the
system begins with significant inhomogeneities on length-scales shorter than
the initial Hubble radius. We incorporate certain nonlinear interactions among
the coupled degrees of freedom by using the nonperturbative Hartree
approximation. Consistent with recent, more computationally intensive
numerical-relativity studies, we find inflation to be robust for large-field
models, even when the system begins with significant structure on sub-Hubble
scales. We consider the space of initial conditions $(\varphi (t_0),
\dot{\varphi} (t_0))$, where $\varphi$ is the vacuum expectation value of the
quantized field that drives inflation. Although some regions of $(\varphi
(t_0), \dot{\varphi} (t_0))$ that would have yielded sufficient inflation in
the absence of inhomogeneities fail to do so when backreaction from
inhomogeneities is incorporated, an equal volume of such regions succeeds in
producing sufficient inflation which did not do so in the absence of
inhomogeneities. For large-field models, in other words, the total volume of
the space of initial conditions $(\varphi (t_0), \dot{\varphi} (t_0))$ that
yields sufficient inflation is {\it conserved} when we incorporate nonlinear
backreaction from inhomogeneities, compared to the case in which
inhomogeneities are neglected.
