Electromagnetic Characterization of Concrete by Jonscher Universal Dielectric Model: Numerical Validation of Different Nonlinear Optimization Algorithms

The dielectric permittivity model of concrete plays a key role in characterizing its interaction with electromagnetic (EM) waves but also in determining its mechanical properties. Among various EM models, the Jonscher universal dielectric response has been favored by scientists and practitioners in the field for the above purposes. Despite its widespread use, to the best of our knowledge, no study has focused its attention on the problem of choosing the most appropriate numerical method and the related starting point solution to solve the nonlinear least squares problem for fitting the Jonscher model to the experimental data. In this work, considering their broad adoption within software packages such as R, Python, or MATLAB, the performances of the Nelder-Mead, the Broyden-Fletcher-Goldfarb-Shanno, and the Levenberg-Marquardt nonlinear optimization algorithms have been compared among them to obtain practical guidance on which nonlinear optimization procedure to choose and how to generate a valid initial guess solution to achieve optimal fitting with the experimental data.