For more than forty years, approximate solutions for the classical pipe network analysis problem have been obtained by direct solution of the nonlinear stationary point conditions. We propose a revolutionary new approach involving optimization techniques for solving this well-known engineering problem. It is shown that the pipe network analysis problem may be described mathematically in terms of a nonlinear convex cost network flow problem. Three mathematical programming algorithms for solving this problem have been coded and are computationally compared with a code using the traditional Newton-Raphson technique. The computational experience demonstrates that this new approach provides an attractive alternative for solving this important problem.
We discuss methods for speeding up convergence of the Frank-Wolfe algorithm for solving nonlinear convex programs. Models involving hydraulic networks, road networks and factory-warehouse networks are described. The PARTAN technique and heuristic variations of the Frank-Wolfe algorithm are described which serve to significantly improve the convergence rate with no significant increase in memory requirements. Computational results for large-scale models are reported.
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