In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex funct...

This paper studies, for a differential variational inequality involving a locally prox-regular set, a regularization process with a family of classical differential equations whose solutions converge to the solution of the differential variational inequality. The concept of local prox-regularity will be termed in a quantified way, as (r, α)-prox-regularity.

The theory of the gap functions is extended to the variational inequality introduced by Minty. Exploiting the minimax formulation of a variational inequality, a new class of gap functions is defined. Descent methods,based on the minimization of the new class of gap functions, are analysed.

In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

In this paper, we present an iterative method for fixed point problems and variational inequality problems. Our method is based on the so-called extragradient method and viscosity approximation method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for monotone mapping.

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has onelayer projection structure and is amenable to parall...

In this paper, the concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variationalhemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed...

In recent years, the variational inequality framework has been recognized as a powerful modelling tool in operations research and economics, whenever equilibrium relationships among several agents occur. This interest has prompted researchers to develop eecient algorithms for solving variational inequalities in nite dimensional spaces. In this presentation we will try to assess the advantages a...

A mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation is introduced and studied, in which the contact is bilateral, the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip, and the behavior of the material is described with a viscoelastic constitutive law wi...

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...