Volume 10, Issue 3
An Algorithm for Finding Nonnegative Minimal Norm Solutions of Linear Systems

S. Bahi & A. Ross


Int. J. Numer. Anal. Mod., 10 (2013), pp. 745-755

Published online: 2013-10

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  • 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 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.

  • Keywords

Linear equations Least norms Optimality Duality conditions

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COPYRIGHT: © Global Science Press

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