A Study Of Bounded Perturbation Resilience And Inertial Modification Of Projection Methods For The Variational Inequality

The variational inequality problem is a basic problem of the optimization method,which is widely applied to the partial differential equation,optimal control,mathematical programming and so on.Variational inequalities have received widespread attention in recent years,and rich achievements have been made in theory and algorithm.In this article,we study the bounded perturbation resilience of the projection class algorithm for the variational inequality problem.We combine the Hilbert space geometry,fixed point theory and variational principle,apply the mathematical tools of the bounded perturbation resilience,projection method and other mathematical tools in this study.The full text is divided into the following parts:First,we study the bounded perturbation resilience of the extragradient-type algorithms.The convergence and convergence rate of the algorithms are proved in theory.Secondly,we construct the inertial correction of extragradient-type algorithms.The effectiveness of the inertial correction of the algorithms are tested by the numerical simulation.Secondly,we study the bounded perturbation resilience of the projection and contraction algorithms.The convergence and convergence rate of the algorithms are proved in theory.And the corresponding inertial correction of the projection and contraction algorithms is constructed,and the accelerated effect of several proposed algorithms is tested by the numerical simulation.Finally,two simultaneous and semi-alternating projection algorithms are proposed for solving split equality problems.The convergence of the algorithms is proved.The results are extended to split feasibility problem.And a numerical example is presented to illustrate the efficiency and advantage of the proposed algorithms.