We show that two antenna array pattern synthesis problems can be expressed as convex optimization problems. The first one deals with a symmetric planar array with real weights, which can be expressed as a linear program. The second one concerns a broadband acoustic array, which becomes a convex quadratically constrained quadratic program. Because these two problems are convex, they can be (numerically) solved with great efficiency by recently developed interior-point methods. Thanks to the efficiency of the interior point methods, we also built a computer-aided design tool for the first problem.