Implementation of Partial Separability in a Source-to-Source Transformation AD Tool

TitleImplementation of Partial Separability in a Source-to-Source Transformation AD Tool
Publication TypeConference Paper
Year of Publication2012
AuthorsNarayanan, SHK, Norris, B, Hovland, PD, Gebremedhin, AH
Conference Name6th International Conference on Automatic Differentiation (AD2012)
Date Published07/2012
Conference LocationFort Collins, CO
Other NumbersANL/MCS-P1997-0112

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.