The structured distance to ill-posedness for conic systems

Adrian S. Lewis

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The structured distance to ill-posedness for conic systems

Adrian S. Lewis

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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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Adrian S. Lewis. 2003-09-05. The structured distance to ill-posedness for conic systems. https://arxiv.org/abs/math/0309100

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