  This paper studies a class of partial information linear-quadratic mean-field
game problems. A general stochastic large-population system is considered,
where the diffusion term of the dynamic of each agent can depend on the state
and control. We study both the control constrained case and unconstrained case.
In control constrained case, by using Hamiltonian approach and convex analysis,
the explicit decentralized strategies can be obtained through projection
operator. The corresponding Hamiltonian type consistency condition system is
derived, which turns out to be a nonlinear mean-field forward-backward
stochastic differential equation with projection operator. The well-posedness
of such kind of equations is proved by using discounting method. Moreover, the
corresponding $\varepsilon$-Nash equilibrium property is verified. In control
unconstrained case, the decentralized strategies can be further represented
explicitly as the feedback of filtered state through Riccati approach. The
existence and uniqueness of a solution to a new Riccati type consistency
condition system is also discussed. As an application, a general inter-bank
borrowing and lending problem is studied to illustrate that the effect of
partial information cannot be ignored.
