Composite Optimization by Nonconvex Majorization-MinimizationCP1

Many tasks in imaging can be modeled as the minimization of non-convex composite functions. Interpreting previous optimization methods as majorization-minimization algorithms show that convex majorizers were previously considered. Yet, certain classes of non-convex majorizers still allow solving each sub-problem to (near)-optimality, leading to a provably convergent optimization scheme. Numerical results illustrate that by applying this scheme, one can achieve superior local optima compared to descent methods, while being significantly more efficient than global optimization methods.

This presentation is part of Contributed Presentation “CP1 - Contributed session 1

Jonas Geiping (University of Siegen)
Michael Moeller (University of Siegen)
inverse problems, nonlinear optimization