AN ALGORITHM FOR COMPUTING NONNEGATIVE MINIMAL NORM SOLUTIONS

In this paper we consider a system of m real linear equations, Ax = b, in n unknowns which has a nonnegative solution. Out of these nonnegative solutions we seek the one which is of least norm when R(n) is equipped with a strictly convex norm. We give a globally convergent, implementable, iterative algorithm converging to the above solution. Within each iteration cycle occurs a quadratic program for minimizing parallel-to x - a(k) parallel-to 2, subject to Ax = b, x greater-than-or-equal-to 0, where the sequence (a(k)) is constructed iteratively. After presenting some duality theorems we prove the convergence of the algorithm. As a special case we test the algorithm for the l(p)-norms (1 < p < infinity Numerical results are also included.