2017/05/03 by Frank Pörner, Pörner, Frank, Daniel Wachsmuth +1
Mathematics · #49K20 #49M20 (Primary) #49N45 (Secondary) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1705.01427
openalex publication_date 2017/05/03 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this article, we consider the Tikhonov regularization of an optimal\ncontrol problem of semilinear partial differential equations with box\nconstraints on the control. We derive a-priori regularization error estimates\nfor the control under suitable conditions. These conditions comprise\nsecond-order sufficient optimality conditions as well as regularity conditions\non the control, which consists of a source condition and a condition on the\nactive sets. In addition, we show that these conditions are necessary for\nconvergence rates under certain conditions. We also consider sparse optimal\ncontrol problems and derive regularization error estimates for them. Numerical\nexperiments underline the theoretical findings.\n