The Research On Convergence Of Solutions For Split Variational Inclusions With Applications

Based on the linear search method in optimization theory,in this thesis,an iteration method,which does not involve in projection operator and the step-sizes do not depend on norm of operator,is firstly proposed to solve the split variational inclusion problem in Hilbert spaces.A weak convergence theorem of the iterative sequence proposed in this thesis to a solution of split variational inclusion problem is obtained.The split minimization problem and split feasibility problem are considered as two applications of our main result in Hilbert space.A simple numerical example is given to demonstrate the convergence of the algorithm.Secondly,inspired by Mann iterative algorithm and Halpern iterative algorithm,draw support from projection operator,a combined iteration algorithm to solve the split variational inclusion problem in Banach spaces is constructed.The strong convergence theorem for solutions of split variational inclusion problem in Banach spaces is obtained,the main result to solve the split minimization problem and split feasibility problem in Banach space is also used.