  A linear-quadratic (LQ, for short) optimal control problem is considered for
mean-field stochastic differential equations with constant coefficients in an
infinite horizon. The stabilizability of the control system is studied followed
by the discussion of the well-posedness of the LQ problem. The optimal control
can be expressed as a linear state feedback involving the state and its mean,
through the solutions of two algebraic Riccati equations. The solvability of
such kind of Riccati equations is investigated by means of semi-definite
programming method.
