A data-independent distance to infeasibility for linear conic systems

TL;DR

This paper introduces a new geometric measure for the well-posedness of homogeneous conic systems, unifying various existing condition measures and providing a deeper geometric understanding.

Contribution

It proposes a data-independent, geometric distance to infeasibility that connects multiple known measures for conic systems, enhancing theoretical insight.

Findings

Unifies several conic system measures through a geometric lens

Provides a new, data-independent distance to infeasibility

Clarifies relationships among well-known condition measures

Abstract

We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system. Our approach sheds new light on and connects several well-known condition measures for conic systems, including {\em Renegar's} distance to infeasibility, the {\em Grassmannian} condition measure, a measure of the {\em most interior} solution, and other geometric measures of {\em symmetry} and of {\em depth} of the conic system.