"Comparison of Different Optimization Algorithms for Nonlinear Inverse Problems in Biomechanics"
Abstract: The aim of this study is to examine the effect on accuracy, efficiency and robustness of using the exact Newton method in comparison to other optimization routines, which are the conjugate gradient and the BFGS algorithms, for an inverse elasticity problem, where the goal is to identify a material parameter field given noisy displacement measurements. First and second order derivatives are necessary which are obtained using adjoint formulations. At the fist step, the direct method is used to compute first order sensitivities of the objective with respect to the material parameters. For calculating second order derivatives, the adjoint approach is used. The methods are applied on two different inverse elasticity problems. It is found that for a reasonable number of material parameters and a low noise level, the Newton method outperforms the other approaches.