Primal-dual Algorithms Of The Split Equality Problems

Split feasible problem can be applied to the CT image restoration technology,medical and computer tomography.Because of its wide application background,it has been studied by many experts and scholars who continue to promote this problem.Experts and scholars have put forward the split common fixed point problem,split equation problem and split equality common fixed-point problem.In this thesis,the author presents new algorithms for solving the the split equality common fixed-point problem of quasi-nonexpansive mappings,split feasible problem of level sets of convex functions,the split common fixed-point problem of averaged mappings and firmly quasi-nonexpansive mappings,and gets the main contents are as follows:Firstly,author uses the dual variable to construct relaxed CQ iterative algorithm and obtains the weak convergence of the proposed algorithm which generalizes the classical CQ algorithm.Then author adapts the viscosity approximation method to modify the CQ iterative algorithm,and obtains the strong convergence of the algorithm.And numerical examples are presented to show the effectiveness of the proposed algorithmSecondly,author uses the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed-point problem of averaged mappings and obtains the weak convergence of the algorithm.Numerical examples are presented to show the effectiveness of the proposed algorithmThirdly,for solving the split equality common fixed-point problem of quasi-nonexpansive mappings,author presents new self-adaptive algorithm which generalizes the simultaneous iterative algorithm and obtains the weak convergence of the algorithm Numerical examples are presented to show the effectiveness of the proposed algorithmFourthly,for solving the split common fixed-point problem of firmly quasi-nonexpansive mappings,author presents the self-adaptive algorithm which combines inertial effects and the primal-dual method.Author obtains the weak convergence of the algorithm.Numerical examples are presented to show the effectiveness of the proposed algorithm.