Ball-Relaxed Projection And Self-adaptive Parameter Selection Method

The iterative algorithm of many nonlinear problem involve the calculation of projection operator as well as the parameter selection problem,whether two problems are handled properly,will directly affect the convergence speed and the convenience of the algorithm.This thesis mainly study the self-adaptive parameter selection method and the ball-relaxed projection method two aspects,solving the problem of block-iterative ART algorithm,the convex feasibility problems,the multiple-sets split feasibility problems and the variational inequality problems.The research results of this article are as follows:Firstly,we propose the best iterative parameters and the optimal selection strategy of block-iterative ART algorithm,respectively.The fastest block-iterative ART algorithm is proposed and the convergence theorem of our algorithm is proved.The numerical experiment are used to illustrate the superiority of the algorithm.Secondly,we propose the parameter self-adaptive iterative algorithm for solving strongly monotone and boundedly Lipschitz continuous variational inequality problems.The convergence theorem of the proposed algorithm is proved and a posteriori error estimate of the convergence rate is obtained.The numerical experiments are used to illustrate the superiority of the algorithm.Thirdly,by mixing the inertial technique,ball-relaxed projection method,selective projection method and CQ algorithm,we present an inertial selection ball-relaxed CQ algorithm for solving the multiple-sets split feasibility problems.The convergence theorem of the proposed algorithm is proved.