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/}
}