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Two properties of condition numbers for convex programs via implicitly defined barrier functions

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Abstract.

We study two issues on condition numbers for convex programs: one has to do with the growth of the condition numbers of the linear equations arising in interior-point algorithms; the other deals with solving conic systems and estimating their distance to infeasibility.¶These two issues share a common ground: the key tool for their development is a simple, novel perspective based on implicitly-defined barrier functions. This tool has potential use in optimization beyond the context of condition numbers.

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Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA, e-mail: jfp@andrew.cmu.edu, , , , , , US

    Javier Peña

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  1. Javier Peña
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Received: October 2000 / Accepted: October 2001¶Published online March 27, 2002

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Peña, J. Two properties of condition numbers for convex programs via implicitly defined barrier functions. Math. Program. 93, 55–75 (2002). https://doi.org/10.1007/s101070200294

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  • DOI: https://doi.org/10.1007/s101070200294

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