The variational inequality problem is reduced to an optimization problem with a di erentiable objective function and simple bounds. Theoretical results are proved, that relate stationary points of the minimization problem to solutions of the variational inequality problem. Perturbations of the original problem are studied and an algorithm that uses the smooth minimization approach for solving m...

We consider variational inequality problems for set-valued vector fields on general Riemannian manifolds. The existence results of the solution, convexity of the solution set, and the convergence property of the proximal point algorithm for the variational inequality problems for set-valued mappings on Riemannian manifolds are established. Applications to convex optimization problems on Riemann...

We describe a new continuation method for the solution of monotone variational inequality problems. The method follows a smooth path which is formed by the solutions of certain perturbed problems. We give some conditions for the existence of this path and present numerical results for variational inequality, convex optimization and complementarity problems.

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 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 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...