Abstract
In this paper, by the nonlinear scalarization method, a global error bound of a weak vector variational inequality is established via a regularized gap function. The result extends some existing results in the literature.MSC:49K40, 90C31.
Highlights
Throughout this paper, let K be a closed convex subset of an Euclidean space Rn and F : Rn → B(Rn, Rm) be a continuously differentiable mapping
Error bounds are to depict the distance from a feasible solution to the solution set, and have played an important role in sensitivity analysis and in convergence analysis of iterative algorithms
Kinds of error bounds have been presented for weak vector variational inequalities in [ – ]
Summary
Throughout this paper, let K be a closed convex subset of an Euclidean space Rn and F : Rn → B(Rn, Rm) be a continuously differentiable mapping. By a regularized gap function and a D-gap function for a weak vector variational inequality, Charitha and Dutta [ ] obtained the error bounds of (WVVI), respectively. In virtue of the regularized gap functions, Sun and Chai [ ] studied some error bounds for generalized (WVVIs). They established an error bound for (WVVI) without the convexity of the constraint set.
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