Convex envelopes for fixed rank approximation
Functional Analysis
2016-08-30 v1
Abstract
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added to the finite rank approximation problem. Expression for the dependence of the convex envelope on the singular values of the given matrix is derived and global minimization properties are derived. The corresponding proximity operator is also studied.
Cite
@article{arxiv.1608.07731,
title = {Convex envelopes for fixed rank approximation},
author = {Fredrik Andersson and Marcus Carlsson and Carl Olsson},
journal= {arXiv preprint arXiv:1608.07731},
year = {2016}
}