A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices
type: Item
instance of: scholarly article
title: A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices
zbMATH Open document ID: 0846.15003
DOI: 10.1016/0024-3795(94)00162-6
author: Bahman Kalantari
published in: Linear Algebra and its Applications
publication date: 1996-04-28T00:00:00Z
review text: It is proved that given a multihomogeneous function satisfying some initial conditions, either it has a certain nonnegative zero over a given subspace, or an associated logarithmic barrier function has a constrained stationary point. Under convexity precisely one of these conditions is satisfied. The derivation of significant properties of the constrained stationary points of the logarithmic barrier function and their relationship to corresponding points of an associated Karmarkar potential function play an important role. The author being from computer science department, could have brought out some numerical applications.
reviewed by: Seshadri Sridhar
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 871253
zbMATH Keywords: diagonal scaling of matrices
zbMATH Keywords: conditioning of matrices
zbMATH Keywords: linear programming
zbMATH Keywords: multihomogeneous function
zbMATH Keywords: logarithmic barrier function
zbMATH Keywords: Karmarkar potential function
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00162-6
OpenAlex ID: W2087472701
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description: scientific article; zbMATH DE number 871253