Error bounds and gap functions for various variational type problems

Upper error bounds of DG-functions for history-dependent variational-hemivariational inequalities

“…Especially, this theory has been applied to different fields of engineering, mechanics, nonsmooth analysis and optimization. In particular, existence results for various kinds of variational-hemivariational inequalities can be found in [17,25,23], the gap functions and error bounds are investigated in [10,14,16,38], the well-posedness and the stability in the sense of convergence are studied in [11,24,41,45,46] and references therein.…”

Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications

“…It is a useful mathematical model which unifies many important concepts in applied mathematics, such as necessary optimality conditions, network equilibrium problems, complementarity problems and systems of nonlinear equations, for instance [3,17,23,50]. Several iterative methods have been developed for solving variational inequalities and related optimization problems, see [10,11,[14][15][16]24,25] and the references therein. In particular, Korpelevich [26] presented the Extragradient method for solving variational inequalities with monotone and Lipschitz continuous mappings in Euclidean space.…”