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The efficient computation of Jacobians represents a fundamental challenge incomputational science and engineering. Large-scale modular numerical simulationprograms can be regarded as sequences of evaluations of in our casedifferentiable modules with corresponding local Jacobians. The latter aretypically not available. Tangent and adjoint versions of the individual modulesare assumed to be given as results of algorithmic differentiation instead. Theclassical (Jacobian) matrix chain product formulation is extended with theoptional evaluation of matrix-free Jacobian-matrix and matrix-Jacobian productsas tangents and adjoints. We propose a dynamic programming algorithm for theminimization of the computational cost of such generalized Jacobian chainproducts without considering constraints on the available persistent systemmemory. In other words, the naive evaluation of an adjoint of the entiresimulation program is assumed to be a feasible option. No checkpointing isrequired. Under the given assumptions we obtain optimal solutions which improvethe best state of the art methods by factors of up to seven on a set ofrandomly generated problem instances of growing size.

Optimization of Generalized Jacobian Chain Products without Memory Constraints