Conic scalarizations for approximate efficient solutions in nonconvex vector optimization problems
type: Item
instance of: scholarly article
title: Conic scalarizations for approximate efficient solutions in nonconvex vector optimization problems
zbMATH Open document ID: 1391.90550
author: Hui Guo
author: Wanli Zhang
published in: Journal of the Operations Research Society of China
publication date: 2018-02-20T00:00:00Z
review text: This paper develops a method to characterize approximate efficient/ weakly efficients and properly efficient points of a set with respect to an improvemennt set. The main tool is the nonlinear scalarization by the functions of the form \(\sup_{y\in -E} ( \langle y^\ast, y\rangle +\alpha \| y\|)\) and \(\inf_{y\in E} ( \langle y^\ast, y\rangle +\alpha \| y\|)\), where \(E\) is the improvement set, \((y^\ast, \alpha)\) is chosen from the augmented dual cones of the ordering cone. The authors present also a correction to a scalarization result in [\textit{R. N. Gasimov}, Lect. Notes Econ. Math. Syst. 507, 189--198 (2001; Zbl 1014.90087)] when the Bishop-Phelps cone is used.
reviewed by: Dinh The Luc
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6841405
zbMATH Keywords: improvement set
zbMATH Keywords: nonlinear scalarization
zbMATH Keywords: approximate efficient points
MaRDI profile type: Publication
full work available at URL: s40305-016-0139-x
OpenAlex ID: W2546952094
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DOI: 10.1007/S40305-016-0139-X
description: scientific article; zbMATH DE number 6841405