Understanding the geometry of infeasible perturbations of a conic linear system

Javier Peña

We discuss some properties of the distance to infeasibility of a conic linear system: $Ax = b, x \in C$, where $C$ is a closed convex cone. Some interesting connections between the distance and the solution of certain optimization problems are established. Such connections provide insight into the estimation of the distance to infeasibility and the explicit computation of infeasible perturbations of a given system. We also investigate the properties of the distance to infeasibility assuming that the perturbations are restricted to have a particular structure.

Contact: jpena@cam.cornell.edu