Reflector antenna optimization using one-sided least-squares

Numerical optimization is commonly used for the design of reflector antennas that produce a contoured beam. The optimization problems that arise in this context are generally nonlinear and difficult to solve to global optimality. Different problem formulations lead to different properties and challenges. We demonstrate that the popular minimax approach can have many local minima and that a local optimization method with a poor initialization may result in a bad design. As an alternative to the minimax approach, we propose a one-sided least-squares formulation. We outline a trust-region method for finding a local minimum, and we illustrate the merits of the new approach with some numerical examples. In particular, our preliminary results indicate that our method is often less sensitive to the initial design than the minimax method. Finally, we investigate the use of the one-sided least-squares model as a means to find an initial guess for the minimax approach, and our results show that it sometimes leads to a better local minimum, and hence improves the design.