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To evaluate system capacity, past works on MultipleInput-Multiple-Output (MIMO) systems with mutually interfering links have focused on maximizing the sum of mutual information as the objective criterion. Since the ultimate goal of a MIMO system is to support network applications used by consumers, we consider the non-concave sigmoid utility function, which is the recommended choice according to Shenker for modeling consumer satisfaction in applications with inelastic network traffic. We formulate the sum of utilities maximization as a global optimization problem with polynomial constraints and a rational objective function. Using a technique known as moment relaxation, we derive a sequence of Semidefinite Programming (SDP) problems whose optimal objective values converge to the global maximum sum of utilities. In our simulation examples, we employ our optimization model to determine the average global maxima sum of utilities by optimizing the covariance matrices of the transmitters. We then compare the results with those attainable by the alternative non-uniform optimal power control model that optimizes only the eigenvalues of the covariance matrices. By examining performance differences between the two models, we obtain insights about how interference and excessive data-rate requirements imposed by the application can impede link-consumers' ability to maximize their sum of utilities.