BibTeX
@ARTICLE{
         Gower2014CtS,
       author = "Gower, Robert Mansel and Mello, Margarida Pinheiro",
       title = "Computing the Sparsity Pattern of {H}essians Using Automatic Differentiation",
       journal = "ACM Transactions on Mathematical Software",
       volume = "40",
       number = "2",
       month = "mar",
       year = "2014",
       issn = "0098-3500",
       pages = "10:1--10:15",
       articleno = "10",
       numpages = "15",
       url = "http://doi.acm.org/10.1145/2490254",
       doi = "10.1145/2490254",
       acmid = "2490254",
       publisher = "ACM",
       address = "New York, NY, USA",
       keywords = "Automatic differentiation, Hessian matrix, second order derivatives, sparsity
         patterns",
       abstract = "We compare two methods that calculate the sparsity pattern of Hessian matrices
         using the computational framework of automatic differentiation. The first method is a forward-mode
         algorithm by Andrea Walther in 2008 which has been implemented as the driver called hess_pat in the
         automatic differentiation package ADOL-C. The second is edge_push_sp, a new reverse mode algorithm
         descended from the edge_pushing algorithm for calculating Hessians by Gower and Mello in 2012. We
         present complexity analysis and perform numerical tests for both algorithms. The results show that
         the new reverse algorithm is very promising.",
       ad_theotech = "Hessian, Sparsity"
}