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First order primal-dual algorithms for nonsmooth optimisation have already demonstrated considerable potential for solving inverse problems in image reconstruction and optimal control. However, their extension to nonlinear forward operators still requires investigation. Based on the idea of testing, we analyse the convergence of a nonlinear extension of the Chambolle-Pock hybrid gradient method in infinite-dimensional Hilbert spaces. We derive step length conditions as well as acceleration rules for suitably point-based monotone problems.
This presentation is part of Minisymposium “MS62 - Imaging models with non-linear constraints (2 parts)”
organized by: Tuomo Valkonen (University of Liverpool) , Juan Carlos De Los Reyes (Escuela Politécnica Nacional) .