Self-adaptive methods for general variational inequalities

Some developments in general mixed quasi variational inequalities

In this paper, we use the resolvent operator to suggest and analyze two new numerical methods for solving general mixed quasi variational inequalities coupled with new directions and new step sizes. Under certain conditions, the global convergence of the both methods is proved. Our results can be viewed as significant extensions of the previously known results for general mixed quasi variationa...

On Self-Adaptive Method for General Mixed Variational Inequalities

We suggest and analyze a new self-adaptive method for solving general mixed variational inequalities, which can be viewed as an improvement of the method of Noor 2003 . Global convergence of the new method is proved under the same assumptions as Noor’s method. Some preliminary computational results are given to illustrate the efficiency of the proposed method. Since the general mixed variationa...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

A New Iterative Method for Solving General Mixed Variational Inequalities

The general mixed variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method cannot be applied to solve this problem due to the presence of the nonlinear term. To overcome this disadvantage, Abedellah Bnouhachem present a self-adaptive iterative method. In this paper, we present a new self-adaptive method w...

A Self–adaptive Projection Method for a Class of Variant Variational Inequalities

In this paper, we consider the general variant variational inequality of the type: Find a vector u∗ ∈ Rn , such that Q(u∗) ∈Ω, 〈v−Q(u∗),Tu∗〉 0, ∀v ∈Ω, where T,Q are operators. We suggest and analyze a very simple self-adaptive iterative method for solving this class of general variational inequalities. Under certain conditions, the global convergence of the proposed method is proved. An example...