A sufficient condition for invexity
type: Item
instance of: scholarly article
title: A sufficient condition for invexity
zbMATH Open document ID: 0671.90070
DOI: 10.1016/0022-247X(89)90329-6
author: Morgan A. Hanson
author: Norma G. Rueda
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The authors consider the problem \[ (1)\quad \min f(x);\quad g(x)\leq 0,\quad x\in X\subset {\mathbb{R}}^ n. \] Invexity at a point u is defined as the existence of a function \(\eta\) (.,.) such that for all x: \(f(x)- f(u)\geq \nabla f(u)^ t\eta (x,u)\). This is a generalization of convexity. Also if at a solution (u,\(\lambda)\) of the first order optimality system, the invexity relation holds for f and all components of g with the same \(\eta\), then u is a global solution of (1). In this paper the authors give sufficient conditions for invexity involving the gradients and lower bounds on the second order variation of the data. As no examples are given it is not easy to evaluate the effectiveness of their results.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4099053
zbMATH Keywords: optimality conditions
zbMATH Keywords: Invexity
zbMATH Keywords: sufficient conditions
zbMATH Keywords: gradients
zbMATH Keywords: second order variation
reviewed by: J. Frédéric Bonnans
MaRDI profile type: Publication
cites work: Invex functions and constrained local minima
cites work: On sufficiency of the Kuhn-Tucker conditions
cites work: Q3682265
full work available at URL: 0022-247x(89)90329-6
OpenAlex ID: W2020770950
description: scientific article; zbMATH DE number 4099053