hess_pat

Computing sparse Hessians with automatic differentiation. 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.

This software is also peer reviewed by journal TOMS.

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References in zbMATH (referenced in 8 articles , 1 standard article )

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  1. Wang, Mu; Gebremedhin, Assefaw; Pothen, Alex: Capitalizing on \textitlivevariables: new algorithms for efficient Hessian computation via automatic differentiation (2016)
  2. Gower, Robert Mansel; Mello, Margarida Pinheiro: Computing the sparsity pattern of Hessians using automatic differentiation (2014)
  3. Kchouk, Bilel; Dussault, Jean-Pierre: On per-iteration complexity of high order Chebyshev methods for sparse functions with banded Hessians (2014)
  4. Walther, Andrea: On the efficient computation of sparsity patterns for Hessians (2012)
  5. Gebremedhin, Assefaw H.; Tarafdar, Arijit; Pothen, Alex; Walther, Andrea: Efficient computation of sparse hessians using coloring and automatic differentiation (2009)
  6. Gebremedhin, Assefaw H.; Pothen, Alex; Walther, Andrea: Exploiting sparsity in Jacobian computation via coloring and automatic differentiation: A case study in a simulated moving bed process (2008)
  7. Walther, Andrea: Computing sparse Hessians with automatic differentiation (2008)
  8. Griewank, Andreas; Juedes, David; Utke, Jean: Algorithm 755: ADOL-C: A package for the automatic differentiation of algorithms written in C/C++ (1996)