Fast Column Generation for Atomic Norm Regularization
Abstract
We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm.
Cite
Text
Vinyes and Obozinski. "Fast Column Generation for Atomic Norm Regularization." International Conference on Artificial Intelligence and Statistics, 2017.Markdown
[Vinyes and Obozinski. "Fast Column Generation for Atomic Norm Regularization." International Conference on Artificial Intelligence and Statistics, 2017.](https://mlanthology.org/aistats/2017/vinyes2017aistats-fast/)BibTeX
@inproceedings{vinyes2017aistats-fast,
title = {{Fast Column Generation for Atomic Norm Regularization}},
author = {Vinyes, Marina and Obozinski, Guillaume},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2017},
pages = {547-556},
url = {https://mlanthology.org/aistats/2017/vinyes2017aistats-fast/}
}