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Yuning Yang(nk0310145gmail.com) Abstract: Inthispaper, weproposetwonewmultiplesetssplitfeasibilityproblem(MSFP)models, where the MSFP requires to find a point closest to the intersection of a family of closed convex sets in one space, such that its image under a linear transformation will be closest to the intersection of another family of closed convex sets in the image space. This problem arises in image restoration, signal processing and intensitymodulated radiation therapy (IMRT). The background of the first new model, called the modified multiplesets split feasibility problem (MMSFP), comes from IMRT. Comparing with MSFP, the MMSFP has three advantages. At the practical level, it is more able to reflect the real world problem; at the algorithmic level, its structure is more separable and the size of each part is smaller, which enables us to apply a modified alternating direction method (ADM) to solve it, which produces parallel steps in each iteration. This parallel feature fits the development of modern parallelarchitecture computers. Then, to overcome the di?culty of computing projections onto the constraint sets, a special version of this method with the strategy of projection onto halfspace is given. The second new model is to find a least l2norm solution of the MSFP (or MMSFP). For this problem, a modified ADM with parallel feature is also provided. The convergence of the three ADMs are established, and the convergence rate of the third method is shown to be O(1/t). Numerical results provide at the last show the e?ciency of our methods. Keywords: multiplesets split feasibility problem, alternating direction method, parallel computing, halfspace, convergence rate Category 1: Complementarity and Variational Inequalities Citation: Download: [PDF] Entry Submitted: 10/09/2012 Modify/Update this entry  
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