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 2 C; where C is a closed convex cone. Some interesting connections between the distance to infeasibility 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. Finally, we extend most of our results to more general conic systems Ax ? b 2 CY ; x 2 CX; where CX and CY are closed, convex cones.