Computable numerical bounds for Lagrange multipliers of stationary points of nonconvex differentiable nonlinear programs
type: Item
instance of: scholarly article
title: Computable numerical bounds for Lagrange multipliers of stationary points of nonconvex differentiable nonlinear programs
zbMATH Open document ID: 0565.90069
DOI: 10.1016/0167-6377(85)90030-6
published in: Operations Research Letters
publication date: 1985-01-01T00:00:00Z
review text: It is shown that the satisfaction of a standard constraint qualification of mathematical programming at a stationary point of a nonconvex differentiable nonlinear program provides explicit numerical bounds for the set of all Lagrange multipliers associated with the stationary point. Solution of a single linear program gives a sharper bound together with an achievable bound on the 1-norm of the multipliers associated with the inequality constraints. The simplicity of obtaining these bounds contrasts sharply with the intractable NP-complete problem of computing an achievable upper bound on the p-norm of the multipliers associated with the equality constraints for integer \(p\geq 1\).
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 3902418
zbMATH Keywords: stationary point
zbMATH Keywords: nonconvex differentiable nonlinear program
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: bounds
author: O. L. Mangasarian
MaRDI profile type: Publication
full work available at URL: 0167-6377(85)90030-6
OpenAlex ID: W2055364214
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description: scientific article; zbMATH DE number 3902418