Stability Analysis Of Some Projection Methods For Variational Inequalities Problems

The thesis mainly discusses the stability analysis of some projection methods for variational inequalities problems.Some scholars have proposed the perturbation analysis of some double projection methods.That shows those double projection methods are stable to a certain extent.The stability analysis of the classic projection methods focuses on two types.One is about the projection method for solving non-monotonic variational inequalities problems and the other is for the classic sub-gradient extragradient projection method proposed by Censor.Chapter 1 introduces the background and present situation of the stability analysis of the projection methods for variational inequalities problems and the main content frame.Chapter 2 introduces some propaedeutics needed by the methods and related assumed conditions and some important definitions.In the third chapter,the stability of the variational inequality projection method in the sense of non-monotonicity is analyzed,and the conclusion that the method can still converge to a solution of the variational inequality under certain perturbation conditions are given.In the fourth chapter,the stability of classical sub-gradient projection method is analyzed,and it is proved that the method can converge to a solution of variational inequalities under certain perturbation conditions.Chapter five summarizes the main content and forecasts the future trends.