Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications
type: Item
instance of: scholarly article
title: Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications
zbMATH Open document ID: 1409.90170
author: Yu Han
author: Nan-Jing Huang
published in: Journal of Optimization Theory and Applications
publication date: 2018-09-04T00:00:00Z
review text: The first part of the paper contains necessary continuity concepts of set-valued mappings and introduces the Gerstewitz's function. In the next part, properties of the nonlinear scalarizing function are studied. The nonlinear scalarizing function is a generalization of Gerstewithz's function introduced by \textit{E. Hernández} and \textit{L. Rodríguez-Marín} [J. Math. Anal. Appl. 325, No. 1, 1--18 (2007; Zbl 1110.90080)]. The main results of the paper consist in conditions, under which continuity and convexity of the nonlinear scalarizing function can be proved. ``The results are applied to proving the upper and lower semicontinuity of strongly approximate solution mappings to the parametric set optimization problems''.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 6931974
zbMATH Keywords: set optimization problem
zbMATH Keywords: nonlinear scalarizing function
zbMATH Keywords: continuity
zbMATH Keywords: convexity
MaRDI profile type: Publication
full work available at URL: s10957-017-1080-9
OpenAlex ID: W2587774467
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DOI: 10.1007/S10957-017-1080-9
description: scientific article; zbMATH DE number 6931974