Proximal Point Methods for the Inverse Problem of Identifying Parameters in Beam Models

This paper studies the nonlinear inverse problem of identifying certain material parameters in the fourth-order boundary value problem representing the beam model. The inverse problem is solved by posing a convex optimization problem whose solution is an approximation of the sought parameters. The optimization problem is solved by the gradient based approaches, and in this setting, the most challenging aspect is the computation of the gradient of the objective functional. We present a detailed treatment of the adjoint stiffness matrix based approach for the gradient computation. We employ recently proposed self-adaptive inexact proximal point methods by Hager and Zhang [6] to solve the inverse problem. It is known that the regularization features of the proximal point methods are quite different from that of the Tikhonov regularization. We present a comparative analysis of the numerical efficiency of the used proximal point methods without using the Tikhonov regularization.