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A New Class of Self-Concordant Barriers from Separable Spectral Functions

Javier Pena(jfp***at***andrew.cmu.edu)
Hristo Sendov(hssendov***at***stats.uwo.ca)

Abstract: Given a separable strongly self-concordant function f:Rn -> R, we show the associated spectral function F(X)= (foL)(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f(x) is separable self-concordant barrier then O^2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O<=22. This generalizes the relationship between the standard logarithmic barriers -log(x1)-...-log(xn) and -log det(X) and gives a partial solution to a conjecture of L. Tuncel.

Keywords: Self-concordant barrier, strongly self-concordant, self-concordant function, spectral function,

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Submitted for publication in Mathematical Programming

Download: [PDF]

Entry Submitted: 09/07/2007
Entry Accepted: 09/07/2007
Entry Last Modified: 09/07/2007

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