On the classical necessary second-order optimality conditions
type: Item
instance of: scholarly article
title: On the classical necessary second-order optimality conditions
zbMATH Open document ID: 1064.90044
published in: Journal of Optimization Theory and Applications
publication date: 2005-04-07T00:00:00Z
review text: In this paper a nonconvex optimization problem in \({\mathbb R}^n\) with equality and inequality constraints is considered. Assuming that the Mangasarian-Fromovitz constraint qualifications hold at a local optimal solution, the aim is to provide sufficient conditions that imply the necessary second-order conditions CN2, with the same Lagrange multipliers. Two main results provide some sufficient conditions; in particular, the second one shows that CN2 holds if the dimension \(n\leq 2\) or if the number of active inequality constraints is at most two. These conditions are sharp, as proved in the counterexample given in the end of the paper.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 2153864
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: Mangasarian-Fromovitz constraint qualifications
zbMATH Keywords: nonconvex optimization
author: Abdeljelil Baccari
reviewed by: Rita Pini
MaRDI profile type: Publication
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DOI: 10.1023/B:JOTA.0000043998.04008.E6
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description: scientific article; zbMATH DE number 2153864