Abstract
We consider the solution of a particular class of nonlinear optimization problems: convex network flows and we show how we have implemented new parallel iterative methods: asynchronous iterations with flexible communication on two types of parallel architectures: a distributed memory supercomputer Cray T3E and a Symmetric Multiprocessor. We deal with asynchronous algorithms whereby every processor can exchange partial updates resulting from intermediate steps of computation with other processors; i.e. every processor can have access to the current value of the components of the iteration vector updated by any other processor. Computational results are presented and analyzed. In particular, the performance of asynchronous iterations with flexible communication is compared with the performance of synchronous and standard asynchronous algorithms.
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