SOME NEW RESOLVENT METHODS FOR SOLVING GENERAL MIXED VARIATIONAL INEQUALITIES
Abdellah Bnouhachem, Muhammad Aslam Noor, Khalida Inayat Noor, Zhaohan Sheng · International Journal of Modern Physics B · 2011
In this paper, we propose two methods for solving general mixed variational inequalities. In the first method, the new iterate is obtained by using a descent direction while the second method can be viewed as an extension of the first one by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. It is proved theoretically that the lower-bound of the progress obtained by the second method is greater than that by the first one. Under certain conditions, the global convergence of the both methods is proved. The comparison of these methods with other methods for solving the mixed genera variational inequalities is an open interesting problem.