Minimax optimization problems have a long and rich history in the area of control. We show how the computation required to find the solution of a popular and widely applicable minimax problem can be significantly reduced. This reduction in computation results from an observation concerning the inner level (finite) maximization. In particular, we show that the number of parameter combinations that must be considered may be significantly reduced, We next indicate how this optimization problem can be used to synthesize a robust state feedback control for a system with parameter uncertainty. We conclude with an example robust control design problem that has 15 independent uncertain parameters and would not be practical were it not for the reduced computational requirement.