Matrix monotonicity and self-concordance: how to handle quantum entropy in optimization problems
type: Item
instance of: scholarly article
title: Matrix monotonicity and self-concordance: how to handle quantum entropy in optimization problems
zbMATH Open document ID: 1394.90529
author: L. Faybusovich
author: Takashi Tsuchiya
published in: Optimization Letters
publication date: 2017-12-15T00:00:00Z
review text: The authors propose a self-concordant barrier for the so-called quantum or von Neumann entropy which is the function \(\text{Tr}(X\, \text{Ln}(X))\) where \(X\) is a positive semi-definite complex Hermitian matrix. This result opens the way for including many optimization problems (arising, e.g., in quantum information theory, quantum statistical physics, information geometry) into a general interior point polynomial framework. The authors consider a broad class of functions, namely, primitives of matrix monotone functions on positive semi-axis. It turns out that the standard \(\ln \det\) barrier is compatible (in the sense of the theory of self-concordant functions) with functions from this class. The authors also establish the self-concordance of associated barriers (along with barrier parameter estimate) on the epigraphs of functions of this class.
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6819050
zbMATH Keywords: quantum entropy
zbMATH Keywords: matrix monotonicity
zbMATH Keywords: self-concordance
reviewed by: R. S. Burachik
MaRDI profile type: Publication
full work available at URL: s11590-017-1145-6
OpenAlex ID: W2607314934
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DOI: 10.1007/S11590-017-1145-6
description: scientific article; zbMATH DE number 6819050