2009/09/28 by Radu Ioan Boţ, Bot, Radu Ioan, Bernd Hofmann +1 · 1 citation
Computer Science · Engineering · Mathematics · #47A52 #47J06 #49N45 #65J20 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.0909.5093
openalex publication_date 2009/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the character of nonlinearity. Recently, the distinguished role of variational inequalities holding on some level sets was outlined for obtaining convergence rates results. When lower rates are expected such inequalities combine the smoothness properties of solution and forward operator in a sophisticated manner. In this paper, using a Banach space setting we are going to extend the variational inequality approach from Hölder rates to more general rates including the case of logarithmic convergence rates.