Abstract
An implementation of the primal-dual predictor-corrector interior point method is specialized to solve block-structured linear programs with side constraints. The block structure of the constraint matrix is exploited via parallel computation. The side constraints require the Cholesky factorization of a dense matrix, where a method that exploits parallelism for the dense Cholesky factorization is used. For testing, multicommodity flow problems were used. The resulting implementation is 65%–90% efficient, depending on the problem instance. For a problem with K commodities, an approximate speedup for the interior point method of 0.8K is realized.
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Lustig, I.J., Li, G. An implementation of a parallel primal-dual interior point method for block-structured linear programs. Comput Optim Applic 1, 141–161 (1992). https://doi.org/10.1007/BF00253804
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DOI: https://doi.org/10.1007/BF00253804