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2014 Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications
Fang Lu, Chun-Rong Chen
Abstr. Appl. Anal. 2014(SI19): 1-10 (2014). DOI: 10.1155/2014/792364


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.


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Fang Lu. Chun-Rong Chen. "Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications." Abstr. Appl. Anal. 2014 (SI19) 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023081
MathSciNet: MR3206820
Digital Object Identifier: 10.1155/2014/792364

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI19 • 2014
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