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In this paper, we address a finite-horizon stochastic optimal control problem with covariance assignment and input energy constraints for discrete-time stochastic linear systems with partial state information. In our approach, we consider separation-based control policies that correspond to sequences of control laws that are affine functions of either the complete history of the output estimation errors, that is, the differences between the actual output measurements and their corresponding estimated outputs produced by a discrete-time Kalman filter, or a truncation of the same history. This particular feedback parametrization allows us to associate the stochastic optimal control problem with a tractable semidefinite (convex) program. We argue that the proposed procedure for the reduction of the stochastic optimal control problem to a convex program has significant advantages in terms of improved scalability and tractability over the approaches proposed in the relevant literature.