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 A. Walther [ACM Trans. Math. Softw. 34, No. 1, Art. 3, 15 p. (2008; Zbl 1291.65190)] 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 R. M. Gower and M. P. Mello [Optim. Methods Softw. 27, No. 2, 251–273 (2012; Zbl 06037758)]. We present complexity analysis and perform numerical tests for both algorithms. The results show that the new reverse algorithm is very promising.

This software is also peer reviewed by journal TOMS.