An iterative row-action method for interval convex programming |
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Authors: | Y Censor A Lent |
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Institution: | (1) Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, New York;(2) Present address: Department of Mathematics, University of Haifa, Mt. Carmel, Haifa, Israel;(3) Present address: New Ventures, Technicare Corp, Cleveland, Ohio |
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Abstract: | The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form minf(x), subject to γ≤Ax≤δ, is proposed. For a certain family of functionsf(x), which includes the norm ∥x∥ and thex logx entropy function, convergence is proved. The present row-action method is particularly suitable for handling problems in which the matrixA is large (or huge) and sparse. |
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Keywords: | Interval convex programming entropy optimization large and sparse matrices nonorthogonal projections image reconstruction from projections |
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