Gradient and extragradient methods for an elliptic inverse problem of parameter identification: A numerical study

In recent years, manygradient and extragradient methods have been studied for minimization problems and variational inequalities. However, only few of them have been implemented and there is currently no understanding of the relative efficiency and effectiveness of these methods. In this paper, we employgradient and extragradient type methods to solve the inverse problem of parameter identification. We present a thorough numerical comparison of projected gradient method, scaled projected gradient method, and several extragradient methods including the Marcotte variants, He-Goldstein type method, the projection-contraction method proposedby Solodov and Tseng, and a hyperplane method.