Exact convergence of a parallel textured algorithm for data network optimal routing problems

In our earlier paper (1991), a textured decomposition based algorithm is developed to solve the optimal routing problem in data networks; a few examples were used to illustrate the speedup advantage and the convergence conditions for the textured algorithm to converge to a global minimum. The speedup advantage is investigated in Huang et al. (1993). However, the theoretical foundation is not provided. In this paper, we provide the foundation. First, we show that for any textured decomposition, the algorithm always converges to a stationary point, which may not be a global minimum. And then, we prove that if the conditions of the exact convergence theorem are satisfied, the textured algorithm will converge to a global minimum