Existence And Uniqueness Theorem And Iteration Methods For A Class Of Inverse Variational Inequality

This thesis proposes and proves a new existence and uniqueness theorem for Lipschitz continuous and strongly monotone inverse variational inequality problem.In addition, through the equivalence inverse variational inequality and variational inequality, The article present double cycle algorithm and relaxed double cycle algorithms for inverse variational inequality problem, because of projection operators on complex closed convex sets are not easy to compute, Then, The article propose operators methods, These algorithms avoid the use of projection operators.The specific content of this paper is organized as follows:Firstly, The thesis research background description, and, The article introduce definition of variational inequalities and inverse variational inequality and the relationship between them, describe he Hilbert space related knowledge of the article briefly, introduce some basic lemmas of the article.Secondly, On the basis of currently available research results, we prove a new existence and uniqueness theorem for Lipschitz continuous and strongly monotone inverse variational inequality problem. The article propose a new double cycle algorithm, prove the strong convergence of iterative algorithm.Lastly, Two new relaxed double cycle iterative algorithms for inverse variational inequality problem are proposed. In order to overcome when closed convex sets more complex, the projection operator is difficult to calculate, the new operators Iterative methods are proposed and the strong convergence theorem are proved.