Stability and Sensitivity Analysis of Solutions to Weak Vector Variational Inequalities

Abstract

The paper mainly concerns the study of a parametric weak vector variational inequality. Robinson's metric regularity and Lipschitzian stability of the solution mapping for the parametric weak vector variational inequality are firstly established. Then sensitivity analysis of the solution mapping for the parametric weak vector variational inequality is discussed. As applications, Lipschitzian continuity and differentiability of the solution mapping are also investigated for a parametric variational inequality.Keywords Robinson's metric regularity · Sensitivity analysis · Parametric weak vector variational inequality · Parametric variational inequality Mathematics Subject Classifications (2010) 49J53 · 90C29 · 90C31

S-derivative of perturbed mapping and solution mapping for parametric vector equilibrium problems

“…Remark 4.1 The results on sensitivity analysis for vector equilibrium problems in Theorem 4.1 and Theorem 4.2 are new because we use the S-derivative of a set-valued mapping, while the other authors [24,25,31] used a contingent derivative and an adaptive subgradient for computing set-valued derivative formulae on some vector optimization problems.…”

“…On the other hand, many scholars have studied sensitivity analysis of vector variational inequalities and vector equilibrium problems by using the concept of contingent derivatives introduced by Aubin [20]. Li et al [21][22][23][24] investigated sensitivity analysis of vector variational inequalities by virtue of a set-valued gap function of parametric vector variational inequalities. Li and Li [25] obtained some results on sensitivity analysis via a set-valued gap function of parametric vector equilibrium problems.…”