Randomized heuristics for exploiting Jacobian scarcity

References

• Griewank , A. 2003 . A mathematical view of automatic differentiation . Acta Numer , 12 : 321 – 398 .
   Google Scholar
• Griewank , A. and Vogel , O. 2005 . “ Analysis and exploitation of Jacobian scarcity ” . In Modeling, Simulation and Optimization of Complex Processes , Edited by: Bock , H. G. , Kostina , E. , Phu , H. X. and Rannacher , R. 149 – 164 . Berlin : Springer .
   Google Scholar
• Griewank , A. and Walther , A. 2008 . “ Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation ” . In Other Titles in Applied Mathematics , 2 , Vol. 105 , Philadelphia, PA : SIAM .
   Google Scholar
• Jerrum , M. and Sinclair , A. 1997 . The Markov Chain Monte Carlo method: An Approach to Approximate Counting and Integration , 482 – 520 . Boston , MA : PWS Publishing Co .
   Google Scholar
• Kirkpatrick , S. Jr. , Gelatt , C. D. and Vecchi , M. P. 1983 . Optimization by simulated annealing . Science , 220 : 671 – 680 .
   PubMed Web of Science ®Google Scholar
• Krishnamoorthy , M. S. and Deo , N. 1979 . Complexity of the minimum-dummy-activities problem in a pert network . Networks , 9 : 189 – 194 .
   Web of Science ®Google Scholar
• Lyons , A. and Utke , J. 2008 . “ On the practical exploitation of scarsity ” . In Advances in Automatic Differentiation , Edited by: Bischof , C. H. , Martin Bücker , H. , Hovland , P. D. , Naumann , U. and Utke , J. Vol. 64 , 103 – 114 . Berlin : Springer . Lecture Notes in Computational Science and Engineering
   Google Scholar
• Metropolis , N. , Rosenbluth , A. W. , Rosenbluth , M. N. , Teller , A. H. and Teller , E. 1953 . Equation of state calculations by fast computing machines . J. Chem. Phys , 21 ( 6 ) : 1087 – 1092 .
   Web of Science ®Google Scholar
• Naumann , U. 2004 . Optimal accumulation of Jacobian matrices by elimination methods on the dual computational graph . Math. Program. Ser. A , 99 ( 3 ) : 399 – 421 .
   Web of Science ®Google Scholar
• Naumann , U. and Gottschling , P. 2001 . “ Prospects for simulated annealing in automatic differentiation ” . In Stochastic Algorithms: Foundations and Applications , Edited by: Steinhöfel , K. Vol. 2264 , 355 – 359 . Berlin : Springer . Lecture Notes in Computer Science
   Google Scholar
• Naumann , U. and Gottschling , P. 2003 . “ Simulated annealing for optimal pivot selection in Jacobian accumulation ” . In Stochastic Algorithms: Foundations and Applications , Edited by: Albrecht , A. and Steinhöfel , K. Vol. 2827 , 83 – 97 . Berlin : Lecture Notes in Computer Science, Springer .
   Google Scholar
• Naumann , U. and Hu , Y. 2008 . Optimal vertex elimination in single-expression-use graphs . ACM Trans. Math. Software , 35 ( 1 ) : 1 – 20 .
   Web of Science ®Google Scholar
• Schneider , J. J. and Kirkpatrick , S. 2006 . Stochastic Optimization (Scientific Computation) , New York : Springer . Inc.
   Google Scholar
• Strassen , V. 1990 . Algebraic Complexity Theory , 633 – 672 . Cambridge , , MA, USA : MIT Press .
   Google Scholar
• Tadjouddine , M. , Bodman , F. , Pryce , J. D. and Forth , S. A. 2005 . “ Improving the performance of the vertex elimination algorithm for derivative calculation ” . In Automatic Differentiation: Applications, Theory, and Implementations , Edited by: Bücker , H. M. , Corliss , G. , Hovland , P. , Naumann , U. and Norris , B. 111 – 120 . Berlin : Springer . Lecture Notes in Computational Science and Engineering
   Google Scholar
• Utke , J. , Naumann , U. , Fagan , M. , Tallent , N. , Strout , M. , Heimbach , P. , Hill , C. and Wunsch , C. 2008 . OpenAD/F: A modular, open-source tool for automatic differentiation of Fortran codes . ACM Trans. Math. Software , 34 ( 4 ) : 18:1 – 18:36 .
   Web of Science ®Google Scholar
• Wong , D. F. , Leong , H. W. and Liu , C. L. 1988 . Simulated Annealing for VLSI Design , Norwell , , MA, USA : Kluwer Academic Publishers .
   Google Scholar