Inverse Design of Wire Antennas Using a Hessian-Based Nonlinear Optimizer with Automatic Differentiation

A Hessian-based approach to perform efficient optimization of wire antennas modelled using Pocklington's integral equation is proposed. We demonstrate how the Hessian matrix of a cost function can be utilized to significantly improve the convergence of an optimizer. The gradient of an antenna parameter is obtained by modifying the Numerical Electromagnetic Code (NEC2) software using a technique called automatic differentiation (AD). This enables us to accurately obtain the derivatives without the need for making significant changes to an existing solver. The gradient of a cost function is computed by a single functional call irrespective of the number of design variables, which makes it very attractive when compared to traditional finite difference methods. The validity of the proposed method is demonstrated by an application example and its advantages are compared with a non-gradient optimization method.