We present an approach to solve the nonconvex optimization problem that arises when designing the transmit covariance matrices in multiuser multiple-input multiple-output (MIMO) broadcast networks implementing simultaneous wireless information and power transfer (SWIPT). The MIMO SWIPT problem is formulated as a general multi-objective optimization problem, in which data rates and harvested powers are optimized simultaneously. Two different approaches are applied to reformulate the (nonconvex) multi-objective problem. In the first approach, the transmitter can control the specific amount of power to be harvested by power transfer whereas in the second approach the transmitter can only control the proportion of power to be harvested among the different harvesting users. The computational complexity will also be different, with higher computational resources required in the first approach. In order to solve the resulting formulations, we propose to use the majorization-minimization (MM) approach. The idea behind this approach is to obtain a convex function that approximates the nonconvex objective and, then, solve a series of convex subproblems that will converge to a locally optimal solution of the general nonconvex multi-objective problem. The solution obtained from the MM approach is compared to the classical block-diagonalization (BD) strategy, typically used to solve the nonconvex multiuser MIMO network by forcing no interference among users. Simulation results show that the proposed approach improves over the BD approach both the system sum rate and the power harvested by users. Additionally, the computational times needed for convergence of the proposed methods are much lower than the ones required for classical gradient-based approaches.