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A data-independent distance to infeasibility for linear conic systems

Javier Pena (jfp***at***andrew.cmu.edu)
Vera Roshchina (v.roshchina***at***unsw.edu.au)

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 into 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, as well as the {\em sigma} and {\em symmetry} measures.

Keywords: condition number, conic programming, distance to infeasibility, convex duality

Category 1: Convex and Nonsmooth Optimization

Citation: Working Paper, Carnegie Mellon University, May 2018.

Download: [PDF]

Entry Submitted: 05/23/2018
Entry Accepted: 05/23/2018
Entry Last Modified: 05/29/2018

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