## 2014.43: Gordon's inequality and condition numbers in conic optimization

2014.43:
Dennis Amelunxen and Martin Lotz
(2014)
*Gordon's inequality and condition numbers in conic optimization.*

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## Abstract

The probabilistic analysis of condition numbers has traditionally been approached from different angles; one is based on Smale's program in complexity theory and features integral geometry, while the other is motivated by geometric functional analysis and makes use of the theory of Gaussian processes. In this note we explore connections between the two approaches in the context of the biconic homogeneous feasiblity problem and the condition numbers motivated by conic optimization theory. Key tools in the analysis are Slepian's and Gordon's comparision inequalities for Gaussian processes, interpreted as monotonicity properties of moment functionals, and their interplay with ideas from conic integral geometry.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | Slepian inequality, Gordon inequality, convex cones, condition number, random matrix theory, convex analysis, geometric functional analysis |

Subjects: | MSC 2000 > 52 Convex and discrete geometry MSC 2000 > 60 Probability theory and stochastic processes MSC 2000 > 65 Numerical analysis MSC 2000 > 90 Operations research, mathematical programming |

MIMS number: | 2014.43 |

Deposited By: | Dr. Martin Lotz |

Deposited On: | 15 August 2014 |

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