  In this paper, we prove the necessary and sufficient maximum principles
(NSMPs in short) for the optimal control of systems described by a quasilinear
stochastic heat equation within convex control domains, which all the
coefficients contain control variables. For that, the optimal control problem
of fully coupled forward-backward doubly stochastic system is studied. We apply
our NSMPs to treat a kind of forward-backward doubly stochastic linear
quadratic optimal control problems and an example of optimal control of
stochastic partial differential equations (SPDEs in short) as well.
