Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy

• Published in: Journal of optimization theory and applications Vol. 194; no. 2; pp. 643 - 680
• Main Authors: Mittal, Gaurav, Giri, Ankik Kumar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer Nature B.V
• Subjects: Accuracy; Algorithms; Applications of Mathematics; Approximation; Banach spaces; Calculus of Variations and Optimal Control; Optimization; Convex analysis; Engineering; Estimates; Ill posed problems; Inverse problems; Iterative methods; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Regularization methods; Stability; Stability constants; Theory of Computation; Inverse problems; Nonlinear ill-posed operator equations; 35R30; 65J22; Multi-level approach; 47J25; Regularization; Iterative regularization methods

In this paper, we introduce a novel nonlinear projected iterative method to solve the ill-posed inverse problems in Banach spaces. This method is motivated by the well-known iteratively regularized Landweber iteration method. We analyze the convergence of our novel method by assuming the conditional...