In this paper, the source and relay transmit covariance matrices are jointly optimized for a fading multiple antenna relay channel when the transmitters only have partial Channel State Information (CSI) in the form of covariance feedback. For full-duplex transmission, the authors evaluate lower and upper bounds on the ergodic channel capacity. These bounds require a joint optimization over the source and relay transmit covariance matrices. The methods utilized in the previous literature fail to find fast and efficient algorithms for the system model considered in this paper. Therefore, they utilize matrix differential calculus in order to solve the joint optimization problem.