This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices Y-i of the form Y-i less than or equal to (Y) over bar(i), where (Y) over bar(i) is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is completely described up to a user-specified parameter. We show that, under suitable assumptions on problem data, the iterative algorithm converges to a solution of the optimality conditions, provided that this parameter is properly chosen. Both discrete- and continuous-time problems are considered.