Abstract
The exploitation of sparsity forms an important ingredient for the efficient solution of large-scale problems. For this purpose, this paper discusses two algorithms to detect the sparsity pattern of Hessians: An approach for the computation of exact sparsity patterns and a second one for the overestimation of sparsity patterns. For both algorithms, corresponding complexity results are stated. Subsequently, new data structures and set operations are presented yielding a new complexity result together with an alternative implementation of the exact approach. For several test problems, the obtained runtimes confirm the new theoretical result, i.e., a significant reduction in the runtime needed by the exact approach. A comparison with the runtime required for the overestimation of the sparsity pattern is included together with a corresponding discussion. Finally, possible directions for future research are stated.
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Walther, A. (2012). On the Efficient Computation of Sparsity Patterns for Hessians. In: Forth, S., Hovland, P., Phipps, E., Utke, J., Walther, A. (eds) Recent Advances in Algorithmic Differentiation. Lecture Notes in Computational Science and Engineering, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30023-3_13
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DOI: https://doi.org/10.1007/978-3-642-30023-3_13
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