Some Projection Methods For Generalized Variational Inequalities

In the first chapter of this dissertation, we investigate the iterative scheme for GMVI(F,f,dom(f)). A different Armijo linesearch is used to con-struct the separating hyperplane in this method. Under some suitable conditions, we prove the convergence theorem. Moreover, we report the preliminary compu-tational experience result. In the second chapter of this dissertation, we suggest a projection method for finding the common point of the fixed point set of a non-expansive mapping and the solution set of generalized variational inequalities (in short, GVIFP). In this method, we construct an new Armijo linesearch and the separating hyperplane. The convergence theorem is established under some mild hypotheses in this part. We, meanwhile, investigate some conditions to ensure that the solution set of GVIFP is nonempty. We also analysis the convergence rate of the iterative sequence under some weaker conditions. Last, we also report the preliminary computational experience result.