An entropy regularization technique for minimizing a sum of Tchebycheff norms
type: Item
instance of: scholarly article
title: An entropy regularization technique for minimizing a sum of Tchebycheff norms
zbMATH Open document ID: 1205.90195
author: Suyan He
author: Yuxi Jiang
author: Shaohua Pan
published in: Applied Numerical Mathematics
publication date: 2010-05-06T00:00:00Z
review text: This paper studies the minimization of a sum of Tchebycheff norms. Since the original formulation of the problem yields a non-smooth objective, the authors propose a smooth approximation based on an entropy function with a smoothing parameter \(\tau\). Subsequently, the resulting smooth minimization problems are solved by a damped Newton method. Driving the smoothing parameter to zero generates a trajectory of optimal solutions that tends to the primal-dual solution set of the original minimization problem. Numerical results for several test problems are shown. Here, the algorithm proposed by the authors is compared with a primal-dual path-following interior point method proposed by \textit{Y. Zhang} [J. Optimization Theory Appl. 77, No. 2, 323--341 (1993; Zbl 0796.49029)].
reviewed by: Andrea Walther
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5704990
zbMATH Keywords: sum of Tchebycheff norms
zbMATH Keywords: entropy regularization
zbMATH Keywords: primal-dual trajectory
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.11.005
OpenAlex ID: W2003881888
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DOI: 10.1016/J.APNUM.2009.11.005
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description: scientific article; zbMATH DE number 5704990