Gordon's inequality and condition numbers in conic optimization

Dennis Amelunxen, Martin Lotz

    Research output: Contribution to journalArticlepeer-review

    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.
    Original languageEnglish
    JournalMIMS EPrints
    Publication statusPublished - Aug 2014

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