A parallel computational model for sensitivity analysis in optimization for robustness

References

• Alber , D. , Graf , P. , Chang , C. H. , Kim , K. and Seibert , M. 2008 . High-performance systems biology: software for metabolic network characterization and optimization over thousands of parameters . submitted for publication
   Google Scholar
• Biros , G. and Ghattas , O. Parallel Newton–Krylov methods for PDE-constrained optimization . Proceedings of Supercomputing 99 . Portland, Or
   Google Scholar
• Brown , P. , Grant , K. , Hindmarsh , A. , Lee , S. , Shumaker , R. S.D. and Woodward , C. 2005 . SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic equation Solvers . ACM Trans. Math. Software , 31 ( 3 ) : 363 – 396 .
   Google Scholar
• Cao , Y. , Li , S. , Petzold , L. and Serban , R. 2003 . Adjoint sensitivity analysis for differential-algebraic equations: the adjoint DAE system and its numerical solution . SIAM J. Sci. Comput. , 24 ( 3 ) : 1076 – 1089 .
   Web of Science ®Google Scholar
• Chang , C. , Alber , D. , Graf , P. , Kim , K. and Seibert , M. 2007 . Addressing unknown constants and metabolic network behaviors through petascale computing: understanding H2 production in green algae . J. Phys.: Conf. Ser. , 78 : 01211 Available at http://www.iop.org/EJ/toc/1742-6596/78/1
   Google Scholar
• Demmel , J. W. , Eisenstat , S. C. , Gilbert , J. R. , Li , X. S. and Liu , J. W.H. 1999 . A supernodal approach to sparse partial pivoting . SIAM J. Matrix Anal. Appli. , 20 : 720 – 755 .
   Web of Science ®Google Scholar
• Dorn , O. , Bertete-Aguirre , H. , Berryman , J. and Papanicolaou , G. 1999 . A nonlinear inversion method for 3D-electromagnetic imaging using adjoint fields . Inverse Probl. , 15 : 1523 – 1558 .
   Web of Science ®Google Scholar
• Feehery , W. , Tolsma , J. and Barton , P. 1997 . Efficient sensitivity analysis of large-scale differential-algebraic systems . Appl. Numer. Math. , 25 ( 1 ) : 41 – 54 .
   Web of Science ®Google Scholar
• Griewank , A. , Juedes , D. and Utke , J. 1996 . Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in c/c++ . ACM Trans. Math. Software , 22 : 131 – 167 .
   Web of Science ®Google Scholar
• Haber , E. and Ascher , U. 2001 . Preconditioned all-at-once methods for large, sparse parameter estimation problems . Inverse Probl. , 17 : 1847 – 1864 .
   Google Scholar
• Haber , E. , Ascher , U. and Oldenburg , D. 2004 . Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach . Geophysics , 69 : 1216 – 1228 .
   Google Scholar
• Hascot , L. and Pascual , V. 2004 . “ Tapenade 2.1 user's guide ” . INRIA . Tech. Rep. 300
   Google Scholar
• Machne , R. , Finney , A. , Muller , S. , Lu , J. , Widder , S. and Flamm , C. 2006 . The SBML ODE solver library: a native API for symbolic and fast numerical analysis of reaction networks . Bioinformatics , 22 : 1406 – 1407 .
   Google Scholar
• Maly , T. and Petzold , L. R. 1997 . Numerical methods and software for sensitivity analysis of differential-algebraic systems . Appl. Numer. Math. , 20 : 57 – 79 .
   Web of Science ®Google Scholar
• Ozyurt , D. and Barton , P. 2005 . Cheap second order directional derivatives of stiff ODE embedded functionals . SIAM J. Sci. Comput. , 26 ( 5 ) : 1725 – 1743 .
   Web of Science ®Google Scholar
• Serban , R. and Hindmarsh , A. CVODES: an ODE solver with sensitivity analysis capabilities . Proceedings of the 5th International Conference on Multibody Systems . Control Long Beach, CA : Nonlinear Dynamics, and .
   Google Scholar
• Serban , R. and Petra , C. 2007 . “ User documentation for IDAS v1.0.0 ” . LLNL . Tech. Rep. UCRL-SM-234051
   Google Scholar
• Vogel , C. 2002 . “ Computational Methods for Inverse Problems ” . Philadelphia, PA : SIAM .
   Google Scholar