Families of differentiable scalarization functions
type: Item
instance of: scholarly article
title: Families of differentiable scalarization functions
zbMATH Open document ID: 0651.90077
DOI: 10.1007/BF00941061
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let F be a family of real-valued maps on \(R^ n\), and let Y be a subset of \(R^ n\). Denote by S(Y\(| F)\) the set of all \(y^*\in Y\) such that, for some \(f\in F\), \(f(y)\geq f(y^*)\) for all y in Y. Let us say that F is a scalarization family if, for any subset Y, S(Y\(| F)\) is equal to the set of properly efficient points in Y. General conditions for F to be a scalarization family were given in a previous paper of the author [J. Optimization Theory Appl. 41, 491-502 (1983; Zbl 0518.90080)]. However, scalarization families must contain nondifferentiable functions. In this note, it is shown that, if the condition of the above-cited paper which forces nondifferentiability is dropped, then S(Y\(| F)\) is dense in the set of properly efficient points.
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 4062845
zbMATH Keywords: multiple criteria optimization
zbMATH Keywords: scalarization methods
zbMATH Keywords: proper efficiency
zbMATH Keywords: scalarization family
zbMATH Keywords: properly efficient points
zbMATH Keywords: nondifferentiability
author: W. B. Gearhart
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00941061
OpenAlex ID: W1996044057
description: scientific article; zbMATH DE number 4062845