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Second derivatives of mathematical models for real-world phenomena arefundamental ingredients of a wide range of numerical simulation methodsincluding parameter sensitivity analysis, uncertainty quantification, nonlinearoptimization and model calibration. The evaluation of such Hessians oftendominates the overall computational effort. The combinatorial {\sc HessianAccumulation} problem aiming to minimize the number of floating-pointoperations required for the computation of a Hessian turns out to beNP-complete. We propose a dynamic programming formulation for the solution of{\sc Hessian Accumulation} over a sub-search space. This approach yieldsimprovements by factors of ten and higher over the state of the art based onsecond-order tangent and adjoint algorithmic differentiation.

Hessian Chain Bracketing