Mathematical Programming

, Volume 112, Issue 2, pp 427–441

Optimal Jacobian accumulation is NP-complete

Authors

    • Software and Tools for Computational Engineering, Department of Computer ScienceRWTH Aachen University
FULL LENGTH PAPER

DOI: 10.1007/s10107-006-0042-z

Cite this article as:
Naumann, U. Math. Program. (2008) 112: 427. doi:10.1007/s10107-006-0042-z

Abstract

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.

Keywords

Automatic differentiation Complexity NP-completeness

Mathematics Subject Classification (2000)

26B10 68Q17

Copyright information

© Springer-Verlag 2006