A projected Newton method for minimization problems with nonlinear inequality constraints
type: Item
instance of: scholarly article
title: A projected Newton method for minimization problems with nonlinear inequality constraints
zbMATH Open document ID: 0632.90058
DOI: 10.1007/BF01396325
author: B. George
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133282
review text: Recently developed projected Newton methods for minimization problems in polyhedrons and Cartesian products of Euclidean balls are extended here to general convex feasible sets defined by finitely many smooth nonlinear inequalities. Iterate sequences generated by this scheme are shown to be locally superlinearly convergent to nonsingular extremals ū, and more specifically, to local minimizers ū satisfying the standard second order Kuhn-Tucker sufficient conditions; moreover, all such convergent iterate sequences eventually enter and remain within the smooth manifold defined by the active constraints at ū. Implementation issues are considered for large scale specially structured nonlinear programs, and in particular, for multistage discrete-time optimal control problems; in the latter case, overall per iteration computational costs will typically increase only linearly with the number of stages. Sample calculations are presented for nonlinear progams in a right circular cylinder in \({\mathbb{R}}^ 3\).
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4029271
zbMATH Keywords: projected Newton methods
zbMATH Keywords: polyhedrons
zbMATH Keywords: smooth nonlinear inequalities
zbMATH Keywords: locally superlinearly convergence
zbMATH Keywords: second order Kuhn-Tucker sufficient conditions
zbMATH Keywords: multistage discrete-time optimal control
zbMATH Keywords: constrained minimization
describes a project that uses: CONOPT
MaRDI profile type: Publication
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OpenAlex ID: W2044362121
description: scientific article; zbMATH DE number 4029271