Mathematical Programming

, Volume 112, Issue 2, pp 427-441

First online:

Optimal Jacobian accumulation is NP-complete

  • Uwe NaumannAffiliated withSoftware and Tools for Computational Engineering, Department of Computer Science, RWTH Aachen University Email author 

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We show that the problem of accumulating Jacobian matrices by using a minimal number of floating-point operations is NP-complete by reduction from Ensemble Computation. The proof makes use of the fact that, deviating from the state-of-the-art assumption, algebraic dependences can exist between the local partial derivatives. It follows immediately that the same problem for directional derivatives, adjoints, and higher derivatives is NP-complete, too.


Automatic differentiation Complexity NP-completeness

Mathematics Subject Classification (2000)

26B10 68Q17