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The Structured Distance to Ill-Posedness for Conic Systems

School of ORIE, Cornell University, Ithaca, New York 14853
aslewis{at}orie.cornell.edu

An important measure of conditioning of a conic linear system is the size of the smallest structured perturbation making the system ill-posed. We show that this measure is unchanged if we restrict to perturbations of low rank. We thereby derive a broad generalization of the classic Eckart-Young result characterizing the distance to ill-posedness for a linear map.

Key Words: condition number; conic system; distance to infeasibility; structured singular values; sublinear maps; surjectivity
History: Received: April 18, 2003; revision received: November 13, 2003;