  This paper investigates the stochastic linear-quadratic control problems with
affine constraints, in which both equality and inequality constraints are
involved. With the help of the Pontryagin maximum principle and Lagrangian
duality theory, the dual problem of original problem is established and the
state feedback form of the solution to the optimal control problem is obtained.
Under the Slater condition, the equivalence is proved between the solutions to
the original problem and the ones of the dual problem, and the KKT condition is
also provided for solving original problem. Especially, a new sufficient
condition is given for the invertibility assumption, which ensures the
uniqueness of the solutions to the dual problem.
