Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 745–755
Abstract
A system of linear equations $Ax = b$, in $n$ unknowns and $m$ equations which has a nonnegative solution is considered. Among all its solutions, the one which has the least norm is sought when $\mathbb{R}^n$ is equipped with a strictly convex norm. We present a globally convergent, iterative algorithm for computing this solution. This algorithm takes into account the special structure of the problem. Each iteration cycle of the algorithm involves the solution of a similar quadratic problem with a modified objective function. Duality conditions for optimality are studied. Feasibility and global convergence of the algorithm are proved. As a special case we implemented and tested the algorithm for the $\ell^p$-norm, where $1 < p < ∞$. Numerical results are included.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-593
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 745–755
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Linear equations Least norms Optimality Duality conditions.