Research On Error Bounds And Algorithms For Solutions Of Mixed Quasi-variational Inequality Problems

Variational inequality problem is an important part of nonlinear analysis,and it is also one of the hot spots in the field of optimization theory.It has been widely used in transportation,bioengineering,and supply chain management.Mixed quasi-variational inequality problems are used as the generalization of variational inequality problems,which includes both mixed variational inequality problems and quasi-variational inequality problems,this type of variational inequality problem is a more generalized model,which is of great research significance.In this paper,we will study the error bounds and projection algorithms for the solutions of two types of variational inequality problems in the n dimensional Euclidean space.The details are as follows:1.In this thesis,we discussed the relationship between the residual gap function of the mixed variational inequality problems and its regularized gap function and D-gap function,and uses the regularized gap function and D-gap function to describe the error bounds for solutions of mixed variational inequality problems.Next,we use the residual gap function to construct a new generalized f-projection algorithm for solving mixed variational inequality problems.Finally,a new projection algorithm is constructed by combining the inertial steps,and through numerical examples verify its validity.2.In this thesis,we use the properties of the generalized f-projection operator.On the one hand,three types of error bounds for relaxed forced mixed quasi-variational inequality problems represented by residual gap functions are established.On the other hand,the three-steps predictive projection algorithm suitable for solving quasi-variational inequality problems is extended to mixed quasi-variational inequality problems.Finally,the strong convergence of the algorithm is proved and a numerical example is given.