Sensitivity Analysis for Relaxed Cocoercive Nonlinear Quasivariational Inclusions

Variational inequality methods whether based on numerous available new algorithms or otherwise have been applied vigorously, especially to model equilibria problems in economics, optimization and control theory, operations research, transportation network modeling, and mathematical programming, while a considerable progress to developing general methods for the sensitivity analysis for variational inequalities is made. Tobin [7] presented the sensitivity analysis for variational inequalities allowing the calculation of derivatives of solution variables with respect to perturbation parameters, where perturbations are of both the variational inequality function and the feasible region. Kyparisis [5] under appropriate second-order and regularity conditions has shown that the perturbed solution to a parametric variational inequality problem is continuous and directionally differentiable with respect to the perturbation parameter. Recently, Agarwal et al. [1] studied the sensitivity analysis for qusivariational inclusions involving strongly monotone mappings applying the resolvent operator technique, without differentiability assumptions on solution variables with respect to perturbation parameters. The aim of this paper is to present the sensitivity analysis for the relaxed cocoercive quasivariational inclusions based on the resolvent operator technique. The obtained results generalize the results on the sensitivity analysis for strongly monotone quasivariational inclusions [1, 2, 6] and others since the class of relaxed cocoercive mappings is more general than the strong monotone mappings, and furthermore, it is less explored. Some suitable