Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces
type: Item
instance of: scholarly article
title: Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces
zbMATH Open document ID: 1095.90105
publication date: 2005-04-07T00:00:00Z
review text: The authors generalize the definition of preinvexity to mappings taking values in a Banach space. They prove a Gordan type alternative theorem for such functions and use it to derive necessary optimality conditions for scalar optimization problems with preinvex objective and constraint functions. These conditions are then extended to vector optimization problems by means of a scalarization result for weakly efficient points of preinvex mappings. Sufficient optimality conditions for such preinvex vector optimization problems are also obtained. Finally, the authors prove that local weakly efficient points of preinvex mappings are necessarily global weakly efficient.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 2153500
zbMATH Keywords: vector optimization
zbMATH Keywords: preinvexity
zbMATH Keywords: optimality conditions
author: L. B. Santos
author: R. Osuna-Gómez
author: Rojas-Medar Marko Antonio
author: A. Rufián-Lizana
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: j.camwa.2003.05.013
OpenAlex ID: W2014238350
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DOI: 10.1016/J.CAMWA.2003.05.013
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2153500