Nonlinear rescaling vs. smoothing technique in convex optimization
type: Item
instance of: scholarly article
title: Nonlinear rescaling vs. smoothing technique in convex optimization
zbMATH Open document ID: 1022.90014
author: Roman A. Polyak
published in: Mathematical Programming. Series A. Series B
publication date: 2003-10-27T00:00:00Z
review text: This article is devoted to convex constrained optimization problems. It analyzes the Log-Sigmoid (LS) multipliers method introduced by the author [Ann. Oper. Res. 101, 427-460 (2001; Zbl 0996.90088)]; in particular, it gives a new convergence proof as well as some estimations of the rate of convergence. These results are extended to the case when a modification of the Chen-Harker-Kanzow-Smale smoothing function is used. For Linear Programming problems having a unique dual solution, the LS method is proved to have a global quadratic rate of convergence. The paper reports some numerical results and concludes by listing some topics left for further research.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 1784735
zbMATH Keywords: constrained optimization
zbMATH Keywords: log-sigmoid multipliers method
zbMATH Keywords: Chen-Harker-Kanzow-Smale smoothing function
zbMATH Keywords: linear programming
zbMATH Keywords: dual problem
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: s101070100293
OpenAlex ID: W2150126561
DOI: 10.1007/S101070100293
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description: scientific article; zbMATH DE number 1784735