The dynamic responses of elastic structures due to vibrations are very important and can produce conditions that can vary from uncomfortable to unsafe. For this reason, optimally designed and placed control devices are very important for the reduction of these vibrations. Many structures have limitations on where these control devices can be placed. However, many existing algorithms are not able to provide solutions to these nonlinear/discrete location problems. A new method is presented for optimal design of the placement and gains of actuators and sensors at discrete locations in output feedback control systems. The method extends the method of Xu et al. (Xu, K., Warnitchai, P., and Ingusa, T., Optimum Locations and Gains of Sensors and Actuators for Feedback Control, AIAA Paper 93-1660, 1993) by solving for the optimal placement at certain discrete locations. A new algorithm is introduced that will allow constrained optimization problems with solutions possible only at discrete locations to be modeled as unconstrained optimization problems. Numerical studies were performed on a two-dimensional structure. Convergence to optimal discrete solutions was efficient.