Projection Algorithms With Inertial Terms For Variational Inequalities

In this thesis,variational inequality problems have been researched in a Hilbert space.The corresponding projection algorithms are proposed for the case where the projection to the feasible set is easy and not easy to calculate,respectively.First,an inertial adaptive subgradient extragradient projection algorithm for solving the variational inequality is proposed when the projection to the feasible set is easily computed.Weak convergence and convergence rate analysis of the algorithm are given for a class of pseudomonotone and Lipschitz continuous mapping,provided by the sequentially weakly continuous mapping.Further,a strong convergence algorithm for solving pseudomonotone variational inequality is demonstrated by introducing a contraction mapping.To show the computational effectiveness of our algorithms,some numerical results are provided.Then,if projections to a feasible set are not easily executed,an inertial relaxation projection algorithm is proposed when is defined on a level set of a convex function.The core of our algorithm is to replace every projection to the feasible set with a projection to some half-space.Weak convergence and convergence rate analysis of the algorithm are proved for a class of monotone and Lipschitz continuous mapping.Further,by introducing a contraction mapping,a strong convergence algorithm is revealed for solving the monotone variational inequality.Numerical experiments are also manifested to show the efficiency and advantages of the proposed algorithms.