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Li, J. and Mastroeni, G. (2010) Vector Variational Inequalities Involving Set-Valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions. Journal of Optimization Theory and Applications, 145, 355-372. https://doi.org/10.1007/s10957-009-9625-1

has been cited by the following article:

• TITLE: Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

  AUTHORS: Rachana Gupta, Aparna Mehra

  KEYWORDS: Set-Valued Vector Quasi Variational Inequality Problem, Gap Function, Regularized Gap Function, Error Bounds, Fixed Point Symmetric Map, α-Holder Map

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 29, 2017

  ABSTRACT: One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.