Modified Double Projection Algorithms For Finding Solutions To Non-monotonic Variational Inequalities

Variational inequalities and common solutions to variational inequality have been applied in many fields in pure mathematics and applied mathematics.Algorithms for solving variational inequalities are interesting and hot research.A lot of algorithms have been proposed.Among them,the projection algorithm and its variants are of importance.The effectiveness and convergence of algorithms depend on conditions of computing variational inequalities.Most algorithms require variational inequalities satisfying some monotonicity or pseudo-monotonicity.A double projection algorithm was proposed by Ye and He for solving variational inequalities without monotonicity.This dissertation studies algorithms for solving variational inequalities without monotonicity.This dissertation is organized as follows:In Chapter 1,the application background,the current situation of variational inequalities,and the main work and contribution of this dissertation are introduced.In Chapter 2,the basic concepts of convex analysis and variational inequalities that will be used in this dissertation,as well as some important properties of projection operators and variational inequalities are recalled.In Chapter 3,an improved double projection algorithm for solving non-monotone variational inequalities is proposed by constructing a new projection region of the projection operator,and the global convergence of the algorithm is proved.The results of the numerical experiments show that the new improved algorithm has better convergence speed and computational efficiency than the known algorithms.In Chapter 4,common solutions to non-monotonic variational inequality problem is analyzed and studied.A projection algorithm for finding common solutions to non-monotonic variational inequalities is proposed,and the convergence of the generated sequence is analyzed.This algorithm generalizes the double projection algorithm for solving non-monotonic variational inequalities to the case of common solutions to non-monotonic variational inequalities.