In this paper, we introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of vector variational inequality and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problem...

Let ugi the unique solutions of an elliptic variational inequality with second member gi (i = 1, 2). We establish necessary and sufficient conditions for the convex combination tug1 + (1 − t)ug2 , to be equal to the unique solution of the same elliptic variational inequality with second member tg1 + (1− t)g2. We also give some examples where this property is valid.

Discontinuous Galerkin (DG) methods are studied for solving an elliptic variational inequality of 4th-order. Numerous discontinuous Galerkin schemes for the Kirchhoff plate bending problem are extended to the variational inequality. Numerical results are presented to illustrate convergence orders of the different methods.

Recently stochastic variational inequality has been extensively studied. However there are few methods can be effectively realized. This study considers to solve stochastic variational inequality by combining quasi-Monte Carlo approach and interior point method. The global convergence is established for the new algorithm. An application for the synergies analysis of the supply chain after M&A f...

We consider the generalized variational inequality and construct certain merit functions associated with this problem. In particular, those merit functions are everywhere nonnegative and their zero-sets are precisely solutions of the variational inequality. We further use those functions to obtain error bounds, i.e., upper estimates for the distance to solutions of the problem.  2003 Elsevier ...

We consider a variational inequality for the Lamé system which models an elastic body in contact with a rigid foundation. We give conditions on the domain and the contact set which allow us to prove regularity of solutions to the variational inequality. In particular, we show that the gradient of the solution is a square integrable function on the boundary.

In this paper, we study the degenerate parabolic variational inequality problem in a bounded domain. First, the weak solutions of the variational inequality are defined. Second, the existence and uniqueness of the solutions in the weak sense are proved by using the penalty method and the reduction method.

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.