Error Bounds for Generalized Multivalued Vector Inverse Quasi-Variational Inequalities via Gap Functions

Abstract

We introduce and analyze a new problem class termed the generalised multivalued vector inverse quasi-variational inequality (GMVIQVI). For this problem, we develop three gap functions: the residual gap function, the regularised gap function, and the \(\mathcal{D}\)-gap function. Under standard assumptions, including strong monotonicity, relaxed monotonicity, and relaxed Lipschitz continuity, we derive explicit error bounds. These bounds are essential, as they enable the estimation of the distance from an arbitrary feasible point to the true solution set of the GMVIQVI. Finally, we shared an example of a numerical technique.