Geometric characterizations for strong minima with applications to nuclear norm minimization problems
Optimization and Control
2023-08-21 v1 Numerical Analysis
Numerical Analysis
Abstract
In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative conditions for this important property. Our characterizations for strong minima are weaker than the Restricted Injectivity and Nondegenerate Source Condition, which are usually used to identify solution uniqueness of nuclear norm minimization problems. Consequently, we obtain the minimum (tight) bound on the number of measurements for (strong) exact recovery of low-rank matrices.
Cite
@article{arxiv.2308.09224,
title = {Geometric characterizations for strong minima with applications to nuclear norm minimization problems},
author = {Jalal Fadili and Tran T. A. Nghia and Duy Nhat Phan},
journal= {arXiv preprint arXiv:2308.09224},
year = {2023}
}
Comments
41 pages