Gradient and Extragradient Methods for an Elliptic Inverse Problem of Parameter Identification: A Numerical Study Gibali Aviv*, Jadamba Baasansuren**, Khan Akhtar A.**, Oleksyn James** *Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, 32000, Israel **Center for Applied and Computational Mathematics, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York, 14623, USA. E-mail: aaksma@rit.edu Abstract In recent years, many gradient 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 employ gradient 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 proposed by Solodov and Tseng, and a hyperplane method. Top Keywords Inverse problems, parameter identification, regularization, projected gradient methods, extragradient methods. Top 2010 Mathematics Subject Classification 47J20, 90C29, 90C30. Top |