We provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index formula can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map (INM) property, which is implied by strong...

A two levels finite element iterative method based on a pressure projection is proposed and analyzed for the transient Navier–Stokes problems. Using the P1–P1 triangular element , we solve a small Navier–Stokes type variational inequality problem on a coarse mesh and solve a large Stokes type variational inequality problem for simple iteration or a large Oseen type variational inequality proble...

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

We derive a global index theorem for degenerate variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index theorem can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map property, which is implied by strong st...

In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of split and composed fixed point problem in real Hilbert spaces. Our uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without prior knowledge operator norm as well Lipschitz constant operator....

In this paper, we consider variational inequality problem over the product of sets which is equivalent to the problem of system of variational inequalities. These two problems are studied for single valued maps as well as for multivalued maps. New concept of pseudomonotonicity in the sense of Brézis is introduced to prove the existence of a solution of our problems. As an application of our res...

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed variational–hemivariational constraints and penalty coefficients. Then, for each inequality, proved unique solvability convergence solutions problems. Following that, proposed mathematical model viscoelastic rod in unila...

We present a scheme which associates to a generalized quasi-variational inequality a dual problem and generalized Kuhn-Tucker conditions. This scheme allows to solve the primal and the dual problems in the spirit of the classical Lagrangian duality for constrained optimization problems and extends, in non necessarily finite dimentional spaces, the duality approach obtained by A. Auslender for g...