Notes on Lipschitz properties of nonlinear scalarization functions with applications
type: Item
instance of: scholarly article
title: Notes on Lipschitz properties of nonlinear scalarization functions with applications
zbMATH Open document ID: 1474.90413
DOI: 10.1155/2014/792364
author: Fang Lu
author: C. R. Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Various kinds of nonlinear scalarization functions play important roles in vector optimization. Among them, the one commonly known as the Gerstewitz function is good at scalarizing. In linear normed spaces, the globally Lipschitz property of such function is deduced via primal and dual spaces approaches, respectively. The equivalence of both expressions for globally Lipschitz constants obtained by primal and dual spaces approaches is established. In particular, when the ordering cone is polyhedral, the expression for calculating Lipschitz constant is given. As direct applications of the Lipschitz property, several sufficient conditions for Hölder continuity of both single-valued and set-valued solution mappings to parametric vector equilibrium problems are obtained using the nonlinear scalarization approach.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 7023081
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describes a project that uses: ASMO
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/792364
OpenAlex ID: W2089331464
Wikidata QID: Q59041518
description: scientific article; zbMATH DE number 7023081