Ill-Conditioned Convex Processes and Conic Linear Systems

We prove the smallest possible norm of a linear perturbation making a closed convex process nonsurjective is the inverse of the norm of the inverse process. This generalizes the fundamental property of the condition number of a linear map. We then apply this result to strengthen a theorem of Renegar measuring the size of perturbation necessary to make a conic linear system inconsistent.

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