This paper presents a fast algorithm for the design of robust output feedback controllers for linear uncertain discrete-time systems. The algorithm utilizes a version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization method of conjugate directions and minimizes a performance index that includes a linear quadratic regulator (LQR) term to optimize performance and a robustness term based on recently developed bounds. The minimization of only the robustness term which corresponds to the maximization of the uncertainty bound is also studied. The case of unstructured perturbations in A has been the only one studied in the robust controller design literature; the present algorithm introduces a unified approach to both cases of unstructured and structured perturbations in the matrices of a state-space model. For the special case of unstructured perturbations in A only, the algorithm is shown to improve considerably the existing unstructured uncertainty bound. Several examples, including an aircraft control system and a paper-machine head box, are presented to illustrate the results.