Alternating direction splittings for block angular parallel optimization

We develop and compare three decomposition algorithms derived from the method of alternating directions. They may be viewed as block Gauss-Seidel variants of augmented Lagrangian approaches that take advantage of block angular structure. From a parallel computation viewpoint, they are ideally suited to a data parallel environment. Numerical results for large-scale multicommodity flow problems are presented to demonstrate the effectiveness of these decomposition algorithms on the Thinking Machines CM-5 parallel supercomputer relative to the widely-used serial optimization package MINOS 5.4. (Author)