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Research of Algorithm for Solving the Multiple-sets Split Feasibility Problem

Author: ZhangZhongWei
Tutor: YangZhenHua
School: Nanjing University of Posts and Telecommunications
Course: Applied Mathematics
Keywords: Multi collection separatist feasible problems Variational inequalities Largest eigenvalue Projection and contraction method
CLC: O224
Type: Master's thesis
Year: 2011
Downloads: 17
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Abstract


More than a collection of split feasibility problem is an important class of optimization problems , abstract mathematical model from the field of image reconstruction and signal processing , has a very important role for the improvement of the efficiency of image and signal processing . People have proposed many solving split feasibility problem , wherein a projection method is a class of basic and important method of calculation , compared with other types of algorithms , the projection algorithm structure is simple, and has a good feasibility . On the basis of extensive research , has a lot of projection -like algorithm . This article focuses on the projection algorithm for solving the split feasibility problem . This article will be split feasibility problem into a specific form of the variational inequality problem , and then to solve the problem of split feasibility algorithm known for solving variational inequalities . And prove the convergence of the algorithm structure . By adding adaptive factor , using different step selection strategies to automatically adjust the step size at each iteration , the iteration step remains in a reasonable range , so that the algorithm has good adaptability . In the structure of the algorithm , there is no need to estimate the matrix spectral radius algorithm . In the numerical experiments , designed CQ algorithm comparison , the numerical results show that the design method for a variety of conditions to have a faster convergence speed , more obvious problem dimension increases . This article is divided into five chapters , the first chapter introduces more than a collection of split feasibility problem definition , the basic form Research ; Chapter II , elaborated used some prior knowledge , will split feasibility problems into linear variational inequality ; third chapter introduces the basic framework of contraction methods , as well as the algorithms used in three basic inequality ; Chapter IV , introduced more than a collection of several split feasibility problem algorithm , algorithm known for solving variational inequalities with in solving the split feasibility problem , given the convergence proof ; Chapter numerical experiments , a comparative analysis of the experimental results of the proposed algorithm .

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