# A structural geometrical analysis of weakly infeasible SDPs

arXiv: https://arxiv.org/abs/1507.06843 · HTML: https://mlsanity.com/paper/1507.06843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [Interior-Point Vanishing Problem in Semidefinite Relaxations for Neural Network Verification](https://mlsanity.com/paper/2506.10269/) (2025)

## Abstract (arXiv)

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 n× n matrices, at most n-1 directions are required to approach the positive semidefinite cone. We also present a discussion on feasibility certificates for SDFPs and related complexity results.