Separable self-concordant spectral functions and a conjecture of Tunçel
type: Item
instance of: scholarly article
title: Separable self-concordant spectral functions and a conjecture of Tunçel
zbMATH Open document ID: 1206.65172
author: Hristo S. Sendov
author: Javier Peña
published in: Mathematical Programming. Series A. Series B
publication date: 2010-10-13T00:00:00Z
review text: The authors show that the associated spectral function \[ F(X)= (f\circ\lambda)(X) \] for a given separable strongly self-concordant function \(f: \mathbb{R}^n\to\mathbb{R}\) is also a strongly self-concordant function. In addition, there is a universal constant \(O\leq 22\) such that if \(f(x)\) is a separable self-concordant barrier, then \(OF(X)\) is a self-concordant barrier. This generalizes the relationship between the \[ -\sum^n_{i=1}\log x_i\text{ and }\log\text{det\,}X \] and gives a partial solution to a conjecture of Tunçel.
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 5799374
zbMATH Keywords: self-concordant barrier
zbMATH Keywords: strongly self-concordant
zbMATH Keywords: self-concordant function
zbMATH Keywords: spectral function
zbMATH Keywords: eigenvalue
zbMATH Keywords: symmetric matrix
Wikidata QID: Q123295889
reviewed by: Hans Benker
MaRDI profile type: Publication
full work available at URL: s10107-008-0260-7
OpenAlex ID: W1973286658
cites work: Q5690490
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DOI: 10.1007/S10107-008-0260-7
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description: scientific article; zbMATH DE number 5799374