Abstract
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 variational inequalities include general variational inequalities, quasivariational inequalities, and nonlinear (implicit) complementarity problems as special cases, results proved in this paper continue to hold for these problems.
Highlights
Variational inequalities introduced in the early sixties have played a critical and significant part in the study of several unrelated problems arising in finance, economics, network analysis, transportation, elasticity, and optimization
Since the general mixed variational inequalities include general variational inequalities, quasivariational inequalities, and nonlinear implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems
T u∗, g v − g u∗ φ g v − φ g u∗ ≥ 0, ∀g v ∈ H, 2.1 which is known as the mixed general variational inequality, see Noor 11
Summary
Variational inequalities introduced in the early sixties have played a critical and significant part in the study of several unrelated problems arising in finance, economics, network analysis, transportation, elasticity, and optimization. The projection method cannot be applied to suggest iterative algorithms for solving general mixed variational inequalities involving the nonlinear term φ. This fact has motivated many authors to develop the auxiliary principle technique for solving the mixed variational inequalities. In 11 , Noor solved the general mixed variational inequality problem by using the resolvent equations technique. Inspired and motivated by the results of Noor 11 , we propose a new method for solving general mixed variational inequalities by using a new direction with a new step size αk. An example is given to illustrate the efficiency and its comparison with the results of Noor 11, 14 This shows that the method is robust and efficient. This new method can be viewed as an important and significant improvement of Noor and other methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
