Research On Fixed Point Algorithms For Split Feasibility Problems And Related Optimization Problems

Optimization has always played an important role in operational research,which is widely used in economy,military,national defense and other fields.In fact,in real life,many problems can be attributed to optimization problems,among which split feasible problem is a kind of common optimization problem.It has become an effective way to study split feasible problem by designing feasible iterative algorithm.In recent years,scholars have also proposed some effective feasible algorithms for this problem.Among these algorithms,the projection algorithm has excellent performance in construction and feasibility.Therefore,this paper proposes a new projection algorithm by improving the existing algorithm,and analyzes the convergence of the algorithm.This paper is divided into two parts:the first part mainly studies the feasibility of solving the splitting problem And the projection algorithm of the fixed point problem of pseudo contractive image.It is proved that the sequence generated by it converges strongly to a common solution of them under appropriate conditions.In the second part,the iterative algorithm for solving the split feasible problem,the variational inequality problem and the fixed point problem is introduced in Hilbert space.The specific contents are as follows:In the first chapter,the author presents introduction and preliminary.the background and research status of splitting feasibility,variational inequality and fixed point are briefly introduced,and the main research contents of this paper are described.In the second chapter,we give two kinds of projection algorithms for splitting feasible problems and fixed point problems,improve the existing results in the existing literature,and analyze the convergence of the algorithm.In the third chapter,we study the iterative algorithms for two kinds of splitting feasible problems,variational inequality problems and fixed point problems,and analyze their convergence.In the fourth chapter,the chapter gives the conclusion and its prospect.