Accelerated Projection Algorithms For Variational Inequalities

In this thesis,we respectively propose accelerated projection algorithms with inertial terms for variational inequality problems in finite dimensional space,when the mapping is quasimonotone on the feasible set and does not have any monotonicity.Firstly,a double projection algorithm for variational inequality problems is proposed when the mapping is quasimonotone on the feasible set.The convergence of the algorithm is proved when the mapping is quasimonotone and non-zero on the feasible set,continuous,and the solution set of the dual variational inequality is non-empty.Furthermore,in order to accelerate the convergence rate of the algorithm,we propose a double projection algorithm with an inertial term for solving quasimonotone variational inequality problems.Under the same conditions,we prove that the convergence of the algorithm.Finally,numerical experiments show the effectiveness of our algorithms.Secondly,when the mapping does not have any monotonicity,we propose a double projection algorithm with an inertial term and a subgradient extragradient projection algorithm with an inertial term.The convergence of our algorithms is proved under appropriate conditions.Finally,numerical experiments show the effectiveness of our algorithms.