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Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-27
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Lu, Fang& Chen, Chun-Rong. 2014. Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014792
Modern Language Association (MLA)
Lu, Fang& Chen, Chun-Rong. Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1014792
American Medical Association (AMA)
Lu, Fang& Chen, Chun-Rong. Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014792
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014792