Duality in nonlinear programs using augmented Lagrangian functions
type: Item
instance of: scholarly article
title: Duality in nonlinear programs using augmented Lagrangian functions
zbMATH Open document ID: 0621.90072
DOI: 10.1016/0022-247X(87)90236-8
author: A. Gonen
author: Mordecai Avriel
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The problem to determine \(V_ p=\min \{f(x)\); \(x\in S\subset R^ n\), \(g_ i(x)=0\), \(i=1,...,m\}\) is considered, by means of the generalized Lagrangian \(L(x,y,r)=f(x)+\phi (g(x),y,r)\), \((y,r)\in R^ m\). Conditions on the augmented multiplier function \(\phi\) are derived, which imply the duality relation \(V_ p=\sup_{y,r} \inf_{x\in S} L(x,y,r)\). These conditions are verified for some particular functions \(\phi\).
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 4008119
zbMATH Keywords: nonconvex optimization
zbMATH Keywords: generalized Lagrangian
zbMATH Keywords: augmented multiplier function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008119