A numerical optimization procedure is applied to two dimensional model of cylindrical reflector antenna arbitrarily located inside a circular cylindrical dielectric radome. If the radome thickness has been optimized, then varying the radome radius and the reflector position has a small effect on the directivity. However, the feed position should be corrected with respect to the free-space optimum after finding the best thickness. The optimization code is based on solving an integral equation by means of the regularization technique, guaranteeing a desired accuracy.