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Exact Convergence of a Parallel Textured Algorithm for Data Network Optimal Routing Problems
November 1995 (vol. 6 no. 11)
pp. 1132-1146

Abstract—In our earlier paper [1], 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 [2]. 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.

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Index Terms:
Exact convergence, Kuhn-Tucker theorem, optimal routing, parallel processing, textured algorithm.
Garng M. Huang, Wen-Lin Hsieh, "Exact Convergence of a Parallel Textured Algorithm for Data Network Optimal Routing Problems," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 11, pp. 1132-1146, Nov. 1995, doi:10.1109/71.476185
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