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The solution of many problems in imaging sciences involves the minimization of a cost function in a feasible convex domain. The latter constraints can be efficiently tackled by adding a logarithmic barrier to the cost function multiplied by a weight tending progressively to zero. We propose a novel interior point method for minimizing a non-smooth convex function under general convex constraints. Its practical efficiency is illustrated through numerical experiments on large scale image recovery applications.
This presentation is part of Minisymposium “MS59 - Approaches for fast optimisation in imaging and inverse problems (3 parts)”
organized by: Jingwei Liang (University of Cambridge) , Carola-Bibiane Schönlieb (University of Cambridge) , Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay) .