We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem, and attempt to find the global optimum solution. As objective functions in UAV path optimization problems tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the purpose of this study, we choose a target tracking application, where the goal is to optimize the kinematic controls of UAVs while maximizing the target tracking performance. First, we compare the performance of two traditional solvers numerically - MATLAB's fmincon and knitro. Second, we formulate this UAV path optimization problem as a mixed-integer nonlinear program (MINLP). As this MINLP tends to be computationally expensive, we present two pruning methods to make this MINLP tractable. We also present numerical results to demonstrate the performance of these methods.