Journal ArticleDOI
An iterative row-action method for interval convex programming
Yair Censor,A. Lent +1 more
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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.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.read more
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Sequential Minimal Optimization : A Fast Algorithm for Training Support Vector Machines
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Mirror descent and nonlinear projected subgradient methods for convex optimization
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TL;DR: It is shown that the MDA can be viewed as a nonlinear projected-subgradient type method, derived from using a general distance-like function instead of the usual Euclidean squared distance, and derived in a simple way convergence and efficiency estimates.
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A multiprojection algorithm using Bregman projections in a product space
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TL;DR: Using an extension of Pierra's product space formalism, it is shown here that a multiprojection algorithm converges and is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem.
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Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems
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References
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The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
TL;DR: This method can be regarded as a generalization of the methods discussed in [1–4] and applied to the approximate solution of problems in linear and convex programming.
Journal ArticleDOI
Row-Action Methods for Huge and Sparse Systems and Their Applications
TL;DR: The main feature of row-action methods is that they are iterative procedures which, without making any changes to the original matrix A, use the rows of A, one row at a time as discussed by the authors.
Journal ArticleDOI
Iterative reconstruction algorithms.
TL;DR: A set of optimization criteria and a number of iterative reconstruction algorithms are stated, together with theorems on the convergence of the algorithms to optimum images and the efficacy of the algorithm is compared to that of the convolution method.
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