We consider several optimization problems that contain the $l_0$-norm expression. These problems are considered to be extremely difficult to solve and analyze due to the nonconvexity and discontinuity of the $l_0$ expression. We establish under some symmetry assumptions a hierarchy between stationarity-based optimality conditions and conditions based on coordinate-wise optimality. These results also imply a hierarchy between several corresponding algorithms. A key mathematical tool used in the analysis is the proximal mapping of symmetric functions including $l_0$-norm expressions.

This presentation is part of Minisymposium “MS55 - Advances of regularization techniques in iterative reconstruction (2 parts)”
organized by: Zichao (Wendy) Di (Argonne National Lab) , Marc Aurèle Gilles (Cornell University) .

Authors:

Amir Beck (Tel-Aviv University)

Nadav Hallak (Technion - Israel Institute of Technology)

Keywords:

inverse problems, machine learning, nonlinear optimization