The Least Squares Problem And The Multiple-matrixes Split Feasibility Problem

The pursuit of optimal goal is the ideals of human beings, with the development of modernproduction and the progress of science and technology, the optimization problem is getting moreattention from people, and now it has penetrated into the area of production, management, business,military, decision etc. However, the least squares problem is a kind of important optimizationproblem. Based on solving multiple-sets split feasibility of projection method, in order to solveconstrained least squares problem, this paper converts constraint least square problem into a specialmultiple-sets split feasibility problem, meanwhile, this paper proposes a projection algorithm. Theprojection algorithm does not need amount of matrix calculations, such as matrix multiplication,and matrix transpose, inverse matrix, which can reduce the workload. The proof of convergenceand numerical tests are also given in this paper. The numerical results show that this method hasfaster convergence speed, good stability and feasibility. In addition, this paper also givesconvergence analysis when projection calculation is not accurate. Based on the conclusion, at last,this paper also puts forward the projection and contraction algorithm for solving themultiple-matrixs split feasibility problem, namely solving different constraint matrix of theoptimization problem. The algorithm talked above is mainly based on the multiple-sets splitfeasibility problem. The author also improves this algorithm, and gives the proof of convergence ofthe two algorithms. Through the numerical tests, feasibility of the two projection algorithms areconfirmed, and the numerical results show that the speed of the improved algorithm convergence isfaster.