Accelerated Antenna Design Methodology Using a Hessian-Based Nonlinear Optimizer With Automatic Differentiation

Abstract

A Hessian-based optimization framework for accelerating the antenna design process is presented. This approach relies on leveraging the second-order derivatives of an objective function to achieve quadratic convergence, offering a significant improvement over gradient-based methods. Instead of computing the Hessian using a finite difference (FD) scheme, a custom-developed method of moments (MoM) solver was integrated with an automatic differentiation (AD) technique to evaluate the gradients at a much lower cost. This implementation requires minimal code modifications, rendering AD a highly attractive choice. Furthermore, when using the gradients in conjunction with the interior point method (IPM), the technique demonstrates superior convergence and requires fewer function evaluations compared to gradient descent (GD) and derivative-free optimization algorithms. This makes the approach very attractive compared to existing methods. Moreover, this method has the added advantage that it can be applied to arbitrary radiation and scattering problems and be readily paired with any optimization method. The accuracy and validity of the proposed method are verified through various application examples.