Understanding the geometry of infeasible
perturbations of a conic linear system
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.