Mathematical Optimization Group, University of Tübingen

$logo.png$

Welcome to the homepage of the

Mathematical Optimization Group

Department of Mathematics, University of Tübingen, Germany

Techniques for gradient based bilevel optimization with nonsmooth lower level problems

Abstract:
We propose techniques for approximating bilevel optimization problems with non-smooth and non-unique lower level problems. The key is the substitution of the lower level minimization problem with an iterative algorithm that is guaranteed to converge to a minimizer of the problem. Using suitable non-linear proximal distance functions, the update mappings of such an iterative algorithm can be differentiable, notwithstanding the fact that the minimization problem is non-smooth. This technique for smoothly approximating the solution map of the lower level problem raises several questions that are discussed in this paper.



pdf	Bibtex	Publisher's link

Citation:
P. Ochs, R. Ranftl, T. Brox, T. Pock:
Techniques for gradient based bilevel optimization with nonsmooth lower level problems.

Journal of Mathematical Imaging and Vision, 56(2):175-194, 2016. (Invited Paper)

Bibtex:
@article{ORBP16, title = {Techniques for gradient based bilevel optimization with nonsmooth lower level problems}, author = {P. Ochs and R. Ranftl and T. Brox and T. Pock}, year = {2016}, journal = {Journal of Mathematical Imaging and Vision}, number = {2}, volume = {56}, pages = {175--194} }