A structural geometrical analysis of weakly infeasible SDPs
Abstract
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of weakly infeasible SDFPs to understand clearly and systematically how weak infeasibility arises in semidefinite programming. In particular, we show that for a weakly infeasible problem over matrices, at most directions are required to approach the positive semidefinite cone. We also present a discussion on feasibility certificates for SDFPs and related complexity results.
Keywords
Cite
@article{arxiv.1507.06843,
title = {A structural geometrical analysis of weakly infeasible SDPs},
author = {Bruno F. Lourenço and Masakazu Muramatsu and Takashi Tsuchiya},
journal= {arXiv preprint arXiv:1507.06843},
year = {2015}
}
Comments
This version contains a shorter and more focused discussion. Proposition 19 and Theorem 23 in the previous version now correspond to Proposition 6 and Theorem 10. We also tried to contextualize some of the results in the BSS model. The first version will stay available at http://www.optimization-online.org/DB_HTML/2013/11/4137.html as well. 14 pages