Overdetermined linear systems satisfying nonnegativity constraints

AbstractLet A be a nonnegative m × n matrix, and let b be a nonnegative vector of dimension m. Also, let S be a subspace of Rn such that if PS is the orthogonal projector onto S, then PS ⩾ 0. A necessary condition is given for the matrix A to satisfy the following property: For all b ⩾ 0, if min[boxV]b − Ax[boxV] is attained at x = x0, then x0 ⩾ 0 and x0 ϵ S. It is also shown that if a nonnegative matrix A has a nonnegative generalized inverse, then any submatrix of A also possesses a nonnegative generalized inverse