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.