CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Algorithms and design for a second-order automatic differentiation module
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
ACM Transactions on Mathematical Software (TOMS)
Computing sparse Hessians with automatic differentiation
ACM Transactions on Mathematical Software (TOMS)
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
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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.