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This paper investigates the optimal design issue of general two-hop amplify-and-forward (AF) MIMO relay networks with one source, one destination and multiple relays, each having multiple antennas. Beginning with the study of the mean-square error (MSE) matrix of the system and the use of Wiener filter for the destination processing, a constrained optimization problem with respect to the unknown relay precoder matrix is formulated with a goal of minimizing the total relay transmit power subject to the MSE-based quality of service (QoS) requirement on each data stream. As the original optimization problem is very difficult to solve, a lower bound of the cost function is pursued to achieve an approximate optimization problem. The modified problem is then solved under the perfect channel state information (CSI) condition using the diagonalization method along with the majorization theory to obtain optimal relay precoder with either nonoptimal or optimal source precoding. It is shown that a convex relay precoding solution is available in the case of nonoptimal source precoding whereas a joint optimal source and relay precoder can be obtained through a multilevel waterfilling algorithm. The optimal design of the relay network under imperfect CSI condition is also considered by modifying the optimization problem with the channel mean and covariance matrix, leading to a robust optimization design of the relay precoder. The proposed technique is validated by Monto Carlo simulations and is also compared with one existing method.