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2014, 4(4): 295-307. doi: 10.3934/naco.2014.4.295

## Nonlinear scalarization with applications to Hölder continuity of approximate solutions

 1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 2 College of Mathematics and Statistics, Chongqing University, Chongqing, 401331

Received  May 2014 Revised  September 2014 Published  December 2014

In this article, firstly, some useful properties of the Gerstewitz scalarizing function are discussed, such as its globally Lipschitz property, concavity and monotonicity. Secondly, as an application of these properties, verifiable sufficient conditions for Hölder continuity of approximate solutions to parametric generalized vector equilibrium problems are established via Gerstewitz scalarizations. Moreover, some examples are provided to illustrate our main conclusions in the vector settings.
Citation: Lili Li, Chunrong Chen. Nonlinear scalarization with applications to Hölder continuity of approximate solutions. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 295-307. doi: 10.3934/naco.2014.4.295
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