Scalarization of Henig properly efficient points in locally convex spaces
type: Item
instance of: scholarly article
title: Scalarization of Henig properly efficient points in locally convex spaces
zbMATH Open document ID: 1206.90166
author: Sumit K. Garg
published in: Journal of Optimization Theory and Applications
publication date: 2010-12-06T00:00:00Z
review text: This paper investigates the scalarization of Henig proper efficiency in the framework of locally convex spaces without any convexity assumption on the feasible sets. By means of the properties of Gerstewitz's function, two versions of scalarizing Henig properly efficient points with respect to a base of the ordering cone are given. Then two further versions of scalarizing generalized Henig properly efficient points and Henig properly efficient points, respectively, are derived which only involve the ordering cone but do not refer to any special base. Since the scalarization results derived in this paper characterize (generalized) Henig properly efficient points by a single functional, any non-convex vector optimization problem defined by Henig proper efficiency can be converted into a scalar optimization problem. Finally, several conditions are derived which guarantee that every generalized Henig properly efficient point is also a Henig properly efficient point.
reviewed by: Frank Werner
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 5823115
zbMATH Keywords: locally convex spaces
zbMATH Keywords: Henig properly efficient points
zbMATH Keywords: scalarization
zbMATH Keywords: Gerstewitz's function
MaRDI profile type: Publication
full work available at URL: s10957-010-9708-z
OpenAlex ID: W2042444161
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DOI: 10.1007/S10957-010-9708-Z
description: scientific article; zbMATH DE number 5823115