Approximate solutions of vector optimization problems via improvement sets in real linear spaces
type: Item
instance of: scholarly article
title: Approximate solutions of vector optimization problems via improvement sets in real linear spaces
zbMATH Open document ID: 1441.90145
author: V. Novo
author: C. Gutiérrez
author: L. Huerga
author: B. Jiménez
published in: Journal of Global Optimization
publication date: 2018-05-25T00:00:00Z
review text: The authors consider the following vector optimization problem: \[ f(x)\longrightarrow \min,\text{ subject to } x \in S, \] where $X$ is an arbitrary decision space, $Y$ is a real linear space ordered by the relation \[ y_1 \leq_{K} y_2 \Longleftrightarrow y_2 -y_1 \in K, \] where $K$ is a convex cone. The notion of improvement is introduced as follows: A nonempty set $E \subset Y$ is said to be an improvement set with respect to $K$ if $E \neq \emptyset$ and $E + K = E$. A point $x^0 \in S$ is said to be $E$-optimal point of the considered vector optimization problem if \[ f(S) - f(x^0) \cap (-E) = \emptyset. \] The authors introduce several modifications of $E$-optimality and study relations between them. The $E$-optimality and its modifications are studied on a real linear space without considering any topology just by using algebraic structures.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 6873202
zbMATH Keywords: vector optimization
zbMATH Keywords: improvement set
zbMATH Keywords: approximate weak efficiency
zbMATH Keywords: approximate proper efficiency
zbMATH Keywords: nearly \(E\)-subconvexlikeness
zbMATH Keywords: linear scalarization
zbMATH Keywords: Lagrange multipliers
zbMATH Keywords: algebraic interior
zbMATH Keywords: vector closure
MaRDI profile type: Publication
full work available at URL: s10898-017-0593-y
OpenAlex ID: W2775168441
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DOI: 10.1007/S10898-017-0593-Y
description: scientific article; zbMATH DE number 6873202