Abstract
Using the primal truncated Newton algorithm for the solution of nonlinear network optimization problems gives rise to very large and sparse systems of linear equations. These systems are solved iteratively with conjugate gradient methods. Using the structural characteristics of the network basis the system of equations is partitioned into independent blocks. Each can be solved in a fraction of the time required for the original equations and can also be solved in parallel. Partitioning schemes are developed for both pure and generalized network problems. Empirical results using problems with up to 15,000 nodes and 37,588 arcs demonstrate the efficiency of the block-partitioning techniques, both for serial and parallel computing. Details of the parallel implementation on a shared-memory multiprocessor, the Alliant FX/4, are given together with computational results on a CRAY X–MP vector supercomputer.
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