The paper presents an optimization-based fixed-order controller design method. A minimization problem is formulated where the objective function is an /(1) - /(infinity) performance measure that quantifies time-domain performance. To achieve an optimization search over all stabilizing fixed-order controllers, a controller parametrization is used that is based on the Youla parametrization and also includes a quadratic equality constraint. The resulting infinite-dimensional optimization problem is nonconvex and is solved by identifying converging sequences of upper and lower bounds. The algorithm is demonstrated through an example. Finally, the paper introduces a global optimization method for the solution of the aforementioned optimization problem. The method is based on the branch-and-bound technique and employs interval analysis to achieve range and dimension reduction in the branching space. Two implementations of interval computations are presented, and the most efficient one consists of a modified interval Newton method that capitalizes on the structure of the problem's equations. The performance of this hybrid method as well as its scaling characteristics are demonstrated through a PI controller optimization example.