Sp. Huestis, NONNEGATIVE SOLUTIONS AND POSITIVE RESOLVING KERNELS WITH NEGATIVE SOLUTION AVERAGES IN LINEAR INVERSE-THEORY, Geophysical journal international, 115(2), 1993, pp. 601-603
Using the duality theorem of linear programming, it is shown that, for
a linear inverse problem, the non-existence of a non-negative solutio
n is equivalent to the existence of a positive-resolving kernel associ
ated with a negative solution average. If no such resolving kernel can
be found, we are then guaranteed the existence of a non-negative solu
tion.