Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 792364, 10 pages.
Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications
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.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 792364, 10 pages.
First available in Project Euclid: 2 October 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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