A general technique for dealing with degeneracy in reduced gradient methods for linearly constrained nonlinear programming
type: Item
instance of: scholarly article
title: A general technique for dealing with degeneracy in reduced gradient methods for linearly constrained nonlinear programming
zbMATH Open document ID: 0802.90098
DOI: 10.1007/BF02006262
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1994-12-12T00:00:00Z
review text: For the nonlinear programming problem `\(f(x)\to\min\)', \(x\in\mathbb{R}\), where \(R= \{x\in \mathbb{R}^ n/Ax= b, x\geq 0\}\) a general model of reduced gradient algorithms is presented. For the given algorithms, non- degeneracy assumptions are not required. Under the assumption of continuous differentiability of the objective function \(f(x)\), the authors prove that either the sequence \(\{x^ k\}\) generated by the algorithm terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of this sequence is a Kuhn-Tucker point.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 597374
zbMATH Keywords: reduced gradient algorithms
zbMATH Keywords: Kuhn-Tucker point
author: Jiye Han
author: Xiaodong Hu
reviewed by: Hans Benker
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02006262
OpenAlex ID: W2005635773
description: scientific article; zbMATH DE number 597374