# Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems

arXiv: https://arxiv.org/abs/1607.05568 · HTML: https://mlsanity.com/paper/1607.05568/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2016.

## 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)

We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can change discontinuously as explained in concrete examples. We show that the optimal value of such a semidefinite program changes continuously under conditions involving the behavior of the minimal faces of the perturbed dual problems. In addition, we determine what kinds of perturbations keep the minimal faces invariant, by using the reducing certificates, which are produced in facial reduction. Our results allow us to classify the behavior of the minimal face of a semidefinite program obtained from a control problem.