TY - JOUR
T1 - An Algorithm for Finding Nonnegative Minimal Norm Solutions of Linear Systems
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 745
EP - 755
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/593.html
KW - Linear equations, Least norms, Optimality, Duality conditions.
AB - <p style="text-align: justify;">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 $1 &lt; p &lt; ∞$. Numerical results are
included.</p>