Vector optimization problems via improvement sets
type: Item
instance of: scholarly article
title: Vector optimization problems via improvement sets
zbMATH Open document ID: 1231.90329
author: F. Mignanego
author: Maurizio Chicco
author: Lucia Pusillo
author: Stef Tijs
published in: Journal of Optimization Theory and Applications
publication date: 2011-11-25T00:00:00Z
review text: The authors introduce the concept of improvement sets and optimal points with respect to the preference relation given by an improvement set (a nonempty set \(E\) in \(\mathbb R^n\) is called an improvement set if it does not contain the origin and has a free disposal property: \(E+\mathbb R^n_+ \subseteq E\); and a point \(a\) of a nonempty set \(A\) in \(\mathbb R^n\) is \(E\)-optimal if \((a+E)\cap A=\emptyset\)). Then they establish some proreties of \(E\)-optimal points and an existence condition by means of separators (linear functions that are strictly positive on \(E\)).
reviewed by: Dinh The Luc
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 5980385
zbMATH Keywords: improvement set
zbMATH Keywords: optimal point
zbMATH Keywords: approximate solution
zbMATH Keywords: free disposal set
MaRDI profile type: Publication
full work available at URL: s10957-011-9851-1
OpenAlex ID: W2072886676
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DOI: 10.1007/S10957-011-9851-1
description: scientific article; zbMATH DE number 5980385