Research On Iterative Methods For A Class Of Variational Inequality Problems

This thesis mainly discusses the iterative algorithms for some special variational inequality problems and discusses the convergence properties of our proposed algorithm.This thesis is divided into five parts: the first part introduces the development of variational inequality theory and the research status and significance of several special variational inequalities.The second part,with the fixed point set of monotone variational inequality iterative technique in real Hilbert space as the foundation,proposed the solution of A special kind of monotone variational inequality problems of double format iteration algorithm,the mapping T is compressed,especially we consider constraint set is great monotone operator is A set of zero,under the constraint of A given strong convergence of the iterative algorithm is analyzed,and for most monotonous operator zero set the minimum norm solution in solving provides A theoretical basis.The third part considers the common solutions of two variational inequalities.In real Hilbert space,based on the Korpelevich extragradient method,a new iterative method is presented to solve the problem of common solutions to two variational inequalities.In the fourth part,a subgradient iterative algorithm is proposed to solve the common solution of the Ky Fan inequality and the fixed point of the pseudo-compression operator in Hilbert space.Under proper constraint assumptions,the proposed algorithm not only has strong convergence but also has better operability and practicability.The last part is the summary of the thesis and the expectation of the future research content,which is expected to get good convergence properties even if the constraint conditions are weakened.However,due to my limited academic level and ability,the research results of this paper still have a lot of room for progress,and the corresponding algorithm mentioned still needs to be further improved.