Gauss-seidel method for least-distance problems |
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| Authors: | W. Li P. M. Pardalos C. G. Han |
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| Affiliation: | (1) Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia;(2) Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida;(3) Department of Computer Science, Pennsylvania State University, University Park, Pennsylvania |
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| Abstract: | ![]()
In this paper, we reformulate the least-distance problems with bounded inequality constraints as an unconstrained convex minimization problem, which is equivalent to a system of piecewise linear equationsA(a+ATy)cd=b. The proposed Gauss-Seidel method for solving the problems is easy to implement and behaves very well when the number of rows ofA is much less than the number of columns ofA. Moreover, we prove that the Gauss-Seidel method has a linear convergence rate.The authors would like to thank Jinshui Qin who did some preliminary numerical testing for their research. |
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| Keywords: | Least-distance problems linear Gauss-Seidel method piecewise linear equations unconstrained convex minimization problems linear convergence |
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