Abstract and Applied Analysis

Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications

Fang Lu and Chun-Rong Chen

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 792364, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278818

Digital Object Identifier
doi:10.1155/2014/792364

Mathematical Reviews number (MathSciNet)
MR3206820

Zentralblatt MATH identifier
07023081

Citation

Lu, Fang; Chen, Chun-Rong. Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 792364, 10 pages. doi:10.1155/2014/792364. https://projecteuclid.org/euclid.aaa/1412278818


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