  A stochastic linear quadratic (LQ) optimal control problem with a pointwise
linear equality constraint on the terminal state is considered. A strong
Lagrangian duality theorem is proved under a uniform convexity condition on the
cost functional and a surjectivity condition on the linear constraint mapping.
Based on the Lagrangian duality, two approaches are proposed to solve the
constrained stochastic LQ problem. First, a theoretical method is given to
construct the closed-form solution by the strong duality. Second, an iterative
algorithm, called augmented Lagrangian method (ALM), is proposed. The strong
convergence of the iterative sequence generated by ALM is proved. In addition,
some sufficient conditions for the surjectivity of the constraint mapping are
obtained.
