The structured distance to ill-posedness for conic systems
Optimization and Control
2025-10-20 v1 Numerical Analysis
Numerical Analysis
Abstract
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 classical Eckart-Young result characterizing the distance to ill-posedness for a linear map.
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@article{arxiv.math/0309100,
title = {The structured distance to ill-posedness for conic systems},
author = {Adrian S. Lewis},
journal= {arXiv preprint arXiv:math/0309100},
year = {2025}
}
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16 pages