S. H. K. Narayanan, B. Norris, P. Hovland, A. Gebremedhin, "Implementation of Partial Separability in a Source-to-Source Transformation AD Tool," Proceedings of AD2012, the 6th International Conference on Automatic Differentiation, 2012. Also Preprint ANL/MCS-P1997-0112, January 2012. [pdf]
A significant number of large optimization problems exhibit structure known as partial separability, for example, least squares problems, where element functions are gathered into groups that are then squared. The sparsity of the Jacobian (and Hessian) of a partially separable function can be exploited by computing the smaller Jacobians of the elemental functions and then assembling them into the full Jacobian. We implemented partial separability support in ADIC2 by using pragmas to identify partially separable function values, applying source transformations to subdivide the elemental gradient computations, and using the ColPack coloring toolkit to compress the sparse elemental Jacobians. We present experimental results for an elastic-plastic torsion optimization problem from the MINPACK-2 test suite.