Iterative Methods For Extended General Mixed Variational Inequalities

Many problems in engineering can be described by general variational inequalities. So the algorithm research for the solution of general variational inequalities is becoming more important. At home and abroad many scholars propose many new kinds of variational inequalities, for example, parametric implicit quasi-variational inequlity, extended general variational inequlities. There are no many research for these new algorithms now, so it has great prospect and significance.In the beginning, we study the three-step iterative algorithm of a class of parametric implicit quasi-variational inequality and discuss the sensitivity of parameter. And then, through the discourse of the benefit function of extended general variational inequalities and its error range, we finally propose a class of new general variational inequalities which can be transferred into corresponding variational inequalities. Its solution can be proved uniqueness using the familiar algorithm, also we have studied its iterations and convergence. The main work is as follows:Firstly, there is the background and current status overview of the variational inequalities and extended general variational inequalities and also introduces the research trends internal and external. The following is some basic concept and conclusion refered in the paper, this lays a theoretical foundation for the research.Secondly, there studies the parametric implicit quasi-variational inequality by using three-step iterative algorithm, and also proved founction solution's convergence. We state the convergence of the algorithm and analysis the sensitivity of parameter.The merit function of extended general variational inequalities has been studied then. We discuss the error range of inequalities' solution through nondifferentiable and differentiable merit function. Finally, a class of new variational inequalities has been proposed. Its solution can be proved uniqueness using the familiar algorithm, also we have studied its iterations and convergence. At last, we discuss six kinds of algorithms and its convergence.