For a multiuser (MU)-MIMO precoded transmission with individual constraints on the maximum power of each transmit antenna, the transmit power optimization problem is a non-linear convex optimization problem with a high level of computational complexity. In this paper, we propose three methods in order to reduce the computational complexity associated with this problem. The reductions in computational complexity achieved with the proposed methods are evaluated under the sum-rate maximization criterion assuming i.i.d Rayleigh fading MIMO channels and block diagonalization zero-forcing as a precoder.