AN ALGORITHM FOR FINDING NONNEGATIVE MINIMAL NORM SOLUTIONS OF LINEAR SYSTEMS

作者：Bahi Said^*; Ross Aaron

来源：International Journal of Numerical Analysis and Modeling, 2013, 10(3): 745-755.

• Linear equations
• Least norms
• Optimality
• Duality conditions

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 l(p)-norm, where 1 < p < infinity. Numerical results are included.

• 出版日期2013