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

Javier Pena (jfp***at***andrew.cmu.edu)

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.

Keywords: convex optimization, barrier functions, implicit functions

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Mathematical Programming 93 (2002) 55--75.

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Entry Submitted: 01/15/2001
Entry Accepted: 01/16/2001
Entry Last Modified: 11/01/2003

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