We consider choice of the regularization parameter in Tikhonov method in the case of the unknown noise level of the data. From known heuristic parameter choice rules often the best results were obtained in the quasi-optimality criterion where the parameter is chosen as the global minimizer of the quasi-optimality function. In some problems this rule fails, the error of the Tikhonov approximation is very large. We prove, that one of the local minimizers of the quasi-optimality function is always a good regularization parameter. We propose an algorithm for finding a proper local minimizer of the quasi-optimality function.
A global minimization algorithm for Tikhonov functionals with sparsity constraints
Jiaxing University（嘉兴学院）；Harbin Institute of Technology（哈尔滨工业大学）；Technische Universität Chemnitz（开姆尼茨工业大学）；Johannes Kepler University（约翰·开普勒大学）；Industrial Mathematics Institute（工业数学研究所）；Johann Radon Institute for Computational and Appied Mathematics（约翰·拉登计算与应用数学研究所）
Inverse initial data reconstruction for a memory convection-diffusion equation via Legendre spatial reduction and Tikhonov regularization
University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；International University - Vietnam National University（越南国立大学国际大学）；Texas A&M University（德克萨斯农工大学）
Elastic energy regularization for inverse obstacle scattering problems
Institute for Numerical and Applied Mathematics, University of Göttingen（哥廷根大学数值与应用数学研究所）；Seminar for Applied Mathematics, ETH Zurich（苏黎世联邦理工学院应用数学科）；Institute for Mathematics, RWTH Aachen University（亚琛工业大学数学研究所）
