Design And Research Of Self-Adaptive Parameter Algorithm For Monotone Variational Inequality

The variational inequality problems are important parts of nonlinear analysis,and their algorithm research is also a hot topic now.Through the design and research of adaptive parameter algorithms in Hilbert space,this thesis mainly constructs two types of iterative algorithm for monotone variational inequalities,that is the monotone variational inequality iteration algorithms for self-adaptive methods(I and II).The strong and weak convergence of the iterative algorithms are proved respectively.The main contents of this paper are as follows:Firstly,three iterative algorithms,based on Tseng algorithm and combining relaxation algorithm and Yamada algorithm,are constructed to solve monotone variational inequality problems.Furthermore,their strong and weak convergence are proved respectively.The validity of the iterative algorithms is verified by the numerical example.Secondly,three iterative algorithms,based on Tseng algorithm and subgradient external gradient method,combined with inertia algorithm and relaxation algorithm,are constructed to solve monotone variational inequality problems.And the weak convergence of these three iterative algorithms is proved respectively.According to numerical examples,the effectiveness and superiority of the iterative algorithm are verified.