On Rutenberg's Decomposition Method

David P. Rutenberg [Rutenberg, David P. 1970. Generalized networks, generalized upper bounding and decomposition of the convex simplex methods. Management Sci.16 (5) 388–401.] provided a method to solve separable nonlinear objective functions with large-scale linear constraints by using W. I. Zangwill's Convex Simplex Method [Zangwill, W. L. 1967. The convex simplex method. Management Sci.14 (3) 221–238.] However, there seem to be several errors in §4.3 [Rutenberg, David P. 1970. Generalized networks, generalized upper bounding and decomposition of the convex simplex methods. Management Sci.16 (5) 397]. Two counterexamples to his conclusions are given in this paper. A revised definition of subproblem, therefore, an optimal criterion of the large-scaled program, is also given.