The cyclic coloring problem and estimation of spare hessian matrices
SIAM Journal on Algebraic and Discrete Methods
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)
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Cheaper Jacobians by Simulated Annealing
SIAM Journal on Optimization
Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
Computing the sparsity pattern of Hessians using automatic differentiation
ACM Transactions on Mathematical Software (TOMS)
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A new approach for computing a sparsity pattern for a Hessian is presented: nonlinearity information is propagated through the function evaluation yielding the nonzero structure. A complexity analysis of the proposed algorithm is given. Once the sparsity pattern is available, coloring algorithms can be applied to compute a seed matrix. To evaluate the product of the Hessian and the seed matrix, a vector version for evaluating second order adjoints is analysed. New drivers of ADOL-C are provided implementing the presented algorithms. Runtime analyses are given for some problems of the CUTE collection.