The Research On Convergence Of Solutions Of The Split Quasi Variational Inclusion Problems With Applications

In optimization theory,the problems of minimization can be transformed into variational inclusion problems of nonlinear set-valued operators.In solving the problems of machine learning,image restoration and signal processing,it can be transformed into quasi variational inclusion problems of the sum of two nonlinear set-valued operators.On the basis of the idea of split feasibility problem,the split quasi variational inclusion problem proposed by Moudafi has been widely used in the model construction of sensor networks,radiation therapy treatment planning and so on.In virtue of thoughts and research experience of scholars,we first investigate the convergence and applications of solutions of the split system of quasi varia-tional inclusion problems in Hilbert spaces.Then,we investigate the convergence and applications of solutions of the split equality quasi variational inclusion prob-lems in uniformly convex and q-uniformly smooth Banach spaces.The results presented in this thesis extend and improve some results in this field.We discuss the following three aspects in this thesis:Firstly,the research background,significance and actualities of the split sys-tem of quasi variational inclusion problems and split equality quasi variational inclusion problems are briefly introduced,and the research content and innova-tion of the problems are expounded;Secondly,by means of the idea of parallel algorithm,parallel hybrid algorithm and forward-backward splitting method,the iterative algorithms are constructed.The convergence of solutions to the split system of quasi variational inclusion problems in Hilbert spaces is studied,and the results of weak convergence and strong convergence of solutions and their applications are obtained;Thirdly,in virtue of the idea of the generalized forward-backward splitting method,the iterative algorithm is constructed.The convergence of solutions to the split equality quasi variational inclusion problems in uniformly convex and q-uniformly smooth Banach spaces is studied,and obtain the strong convergence results of solutions and their applications.