  A Linear-quadratic optimal control problem is considered for mean-field
stochastic differential equations with deterministic coefficients. By a
variational method, the optimality system is derived, which turns out to be a
linear mean-field forward-backward stochastic differential equation. Using a
decoupling technique, two Riccati differential equations are obtained, which
are uniquely solvable under certain conditions. Then a feedback representation
is obtained for the optimal control.
