NONLINEAR SCALARIZATION WITH APPLICATIONS TO HOLDER CONTINUITY OF APPROXIMATE SOLUTIONS

摘要

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 Holder 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.