Dakota Reference Manual: Bibliographic References

| Dakota Reference Manual Version 6.15 Explore and Predict with Confidence

- Main Page
- Related Pages

All Pages
Bibliographic References

[1]

  M.A. Abramson, C. Audet, G. Couture, J.E. Dennis, Jr., S. Le Digabel, and C. Tribes. The NOMAD project. Software available at http://www.gerad.ca/nomad.

[2]

  B. M. Adams, W. J. Bohnhoff, R. A. Canfield, K. R. Dalbey, M. S. Ebeida, J. P. Eddy, M. S. Eldred, G. Geraci, R. W. Hooper, P. D. Hough, K. T. Hu, J. D. Jakeman, K. Carson, M. Khalil, K. A. Maupin, J. A. Monschke, E. M. Ridgway, A. A. Rushdi, D. T. Seidl, J. A. Stephens, L. P. Swiler, A. Tran, D. M. Vigil, T. M. Wildey, J. G. Winokur, and (with Menhorn, F. and Zeng, X.). Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.14 Reference Manual. Sandia National Laboratories, Albuquerque, NM, May 2021. Available online from http://dakota.sandia.gov/documentation.html.

[3]

  B. M. Adams, W. J. Bohnhoff, R. A. Canfield, K. R. Dalbey, M. S. Ebeida, J. P. Eddy, M. S. Eldred, G. Geraci, R. W. Hooper, P. D. Hough, K. T. Hu, J. D. Jakeman, K. Carson, M. Khalil, K. A. Maupin, J. A. Monschke, E. M. Ridgway, A. A. Rushdi, D. T. Seidl, J. A. Stephens, L. P. Swiler, A. Tran, D. M. Vigil, T. M. Wildey, J. G. Winokur, and (with Menhorn, F. and Zeng, X.). Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.14 Developers Manual. Sandia National Laboratories, Albuquerque, NM, May 2021. Available online from http://dakota.sandia.gov/documentation.html.

[4]

  B. M. Adams, W. J. Bohnhoff, K. R. Dalbey, M. S. Ebeida, J. P. Eddy, M. S. Eldred, R. W. Hooper, P. D. Hough, K. T. Hu, J. D. Jakeman, M. Khalil, K. A. Maupin, J. A. Monschke, E. M. Ridgway, A. A. Rushdi, D. T. Seidl, J. A. Stephens, L. P. Swiler, and J. G. Winokur. Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 6.14 users manual. Technical Report SAND2021-5822, Sandia National Laboratories, Albuquerque, NM, May 2021. Available online from http://dakota.sandia.gov/documentation.html.

[5]

  G. Anderson and P. Anderson. The UNIX C Shell Field Guide. Prentice-Hall, Englewood Cliffs, NJ, 1986.

[6]

  J. S. Arora. Introduction to Optimum Design. McGraw-Hill, New York, 1989.

[7]

  C. Audet, S. Le Digabel, and C. Tribes. NOMAD user guide. Technical Report G-2009-37, Les cahiers du GERAD, 2009.

[8]

  J.-P. Berrut and L. N. Trefethen. Barycentric lagrange interpolation. SIAM Review, 46(3):501–517, 2004.

[9]

  B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. McFarland. Multimodal reliability assessment for complex engineering applications using efficient global optimization. In Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (9th AIAA Non-Deterministic Approaches Conference), number AIAA-2007-1946, Honolulu, HI, April 2007.

[10]

  B. J. Bichon, M. S. Eldred, L. P. Swiler, S. Mahadevan, and J. M. McFarland. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA Journal, 46(10):2459–2468, 2008.

[11]

  K. Breitung. Asymptotic approximation for multinormal integrals. J. Eng. Mech., ASCE, 110(3):357–366, 1984.

[12]

  R. H. Byrd, R. B. Schnabel, and G. A. Schultz. Parallel quasi-newton methods for unconstrained optimization. Mathematical Programming, 42:273–306, 1988.

[13]

  K. J. Chang, R. T. Haftka, G. L. Giles, and P.-J. Kao. Sensitivity-based scaling for approximating structural response. J. Aircraft, 30:283–288, 1993.

[14]

  A. R. Conn, N. I. M. Gould, and P. L. Toint. Trust-Region Methods. MPS-SIAM Series on Optimization, SIAM-MPS, Philadelphia, 2000.

[15]

  K. R. Dalbey, M. S. Eldred, J. D. Geraci, G. Jakeman, K. A. Maupin, J. A. Monschke, D. T. Seidl, L. P. Swiler, A. Tran, and (with Menhorn, F. and Zeng, X.). Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 6.14 theory manual. Technical Report SAND2021-5821, Sandia National Laboratories, Albuquerque, NM, May 2021. Available online from http://dakota.sandia.gov/documentation.html.

[16]

  A. Der Kiureghian and P. L. Liu. Structural reliability under incomplete information. J. Eng. Mech., ASCE, 112(EM-1):85–104, 1986.

[17]

  Q. Du, V. Faber, and M. Gunzburger. Centroidal voronoi tessellations: Applications and algorithms. SIAM Review, 41:637–676, 1999.

[18]

  J. E. Eddy and K. Lewis. Effective generation of pareto sets using genetic programming. In Proceedings of ASME Design Engineering Technical Conference, 2001.

[19]

  A. S. El-Bakry, R. A. Tapia, T. Tsuchiya, and Y. Zhang. On the formulation and theory of the newton interior-point method for nonlinear programming. Journal of Optimization Theory and Applications, 89:507–541, 1996.

[20]

  M. S. Eldred and B. J. Bichon. Second-order reliability formulations in DAKOTA/UQ. In Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, number AIAA-2006-1828, Newport, RI, May 1–4 2006.

[21]

  M. S. Eldred and D. M. Dunlavy. Formulations for surrogate-based optimization with data fit, multifidelity, and reduced-order models. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, number AIAA-2006-7117, Portsmouth, VA, September 6–8 2006.

[22]

  M. S. Eldred, A. A. Giunta, and S. S. Collis. Second-order corrections for surrogate-based optimization with model hierarchies. In Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY,, Aug. 30–Sept. 1, 2004. AIAA Paper 2004-4457.

[23]

  M. S. Eldred, H. Agarwal, V. M. Perez, S. F. Wojtkiewicz, Jr., and J. E. Renaud. Investigation of reliability method formulations in DAKOTA/UQ. Structure & Infrastructure Engineering: Maintenance, Management, Life-Cycle Design & Performance, 3(3):199–213, 2007.

[24]

  G. M. Fadel, M. F. Riley, and J.-F. M. Barthelemy. Two point exponential approximation method for structural optimization. Structural Optimization, 2(2):117–124, 1990.

[25]

  R. Fourer, D. M. Gay, and B. W. Kernighan. AMPL: A Modeling Language for Mathematical Programming, 2nd ed.. Duxbury Press/Brooks/Cole Publishing Co., Pacific Grove, CA, 2003. For small examples, e.g., at most 300 variables, a student version of AMPL suffices; see `http://www.ampl.com/DOWNLOADS`.

[26]

  J. H. Friedman. Multivariate adaptive regression splines. Annals of Statistics, 19(1):1–141, March 1991.

[27]

  J. Gablonsky. Direct version 2.0 userguide technical report. Technical Report CRSC-TR01-08, North Carolina State University, Center for Research in Scientific Computation, Raleigh, NC, 2001.

[28]

  D. M. Gay. Hooking your solver to AMPL. Technical Report Technical Report 97-4-06, Bell Laboratories, Murray Hill, NJ,

  1. Available online as http://www.ampl.com/REFS/HOOKING/index.html and http://www.ampl.com/REFS/hooking2.pdf and http://www.ampl.com/REFS/hooking2.ps.gz.

[29]

  D. M. Gay. Specifying and reading program input with NIDR. Technical Report SAND2008-2261P, Sandia National Laboratories, 2008. Available as http://dakota.sandia.gov/papers/nidr08.pdf.

[30]

  R. Ghanem and J. R. Red-Horse. Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element technique. Physica D, 133:137–144, 1999.

[31]

  R. G. Ghanem and P. D. Spanos. Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, New York, 1991.

[32]

  P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization. Academic Press, San Diego, CA, 1981.

[33]

  P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. User's guide for NPSOL (Version 4.0): A Fortran package for nonlinear programming. Technical Report TR SOL-86-2, System Optimization Laboratory, Stanford University, Stanford, CA, 1986.

[34]

  A. A. Giunta, L. P. Swiler, S. L Brown, M. S. Eldred, M. D. Richards, and E. C. Cyr. The surfpack software library for surrogate modeling of sparse, irregularly spaced multidimensional data. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, number AIAA-2006-7049, Portsmouth, VA, 2006.

[35]

  A. A. Giunta. Use of data sampling, surrogate models, and numerical optimization in engineering design. In Proc. 40th AIAA Aerospace Science Meeting and Exhibit, number AIAA-2002-0538, Reno, NV, January 2002.

[36]

  Alex A. Gorodetsky, Gianluca Geraci, Michael S. Eldred, and John D. Jakeman. A generalized approximate control variate framework for multifidelity uncertainty quantification. Journal of Computational Physics, 408:109257, 2020.

[37]

  G. A. Gray and T. G. Kolda. Algorithm 856: APPSPACK 4.0: Asynchronous parallel pattern search for derivative-free optimization. ACM Transactions on Mathematical Software, 32(3):485–507, September 2006.

[38]

  M. Gunburger and J. Burkardt. Uniformity measures for point samples in hypercubes, 2004. Available on John Burkardt's web site: http://www.csit.fsu.edu/&nbsp;burkardt/.

[39]

  Heikki Haario, Marko Laine, Antonietta Mira, and Eero Saksman. DRAM: Efficient adaptive MCMC. Statistics and Computing, 16:339–354, 2006.

[40]

  R. T. Haftka and Z. Gurdal. Elements of Structural Optimization. Kluwer, Boston, 1992.

[41]

  R. T. Haftka. Combining global and local approximations. AIAA Journal, 29(9):1523–1525, 1991.

[42]

  A. Haldar and S. Mahadevan. Probability, Reliability, and Statistical Methods in Engineering Design. Wiley, New York, 2000.

[43]

  J. H. Halton and G. B. Smith. Algorithm 247: Radical-inverse quasi-random point sequence. Communications of the ACM, 7:701–702, 1964.

[44]

  J. H. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik, 2:84–90, 1960.

[45]

  W. E. Hart, A. A. Giunta, A. G. Salinger, and B. G. van Bloemen Waanders. An overview of the adaptive pattern search algorithm and its application to engineering optimization problems. In Proceedings of the McMaster Optimization Conference: Theory and Applications, Hamilton, Ontario, Canada, 2001.

[46]

  J. C. Helton and F. J. Davis. Sampling-based methods for uncertainty and sensitivity analysis. Technical Report SAND99-2240, Sandia National Laboratories, Albuquerque, NM, 2000.

[47]

  J. C. Helton and W. L. Oberkampf. Special issue of reliability engineering and system safety: Issue on alternative representations of epistemic uncertainty, Jul–Sep 2004.

[48]

  D. Higdon, J. Gattiker, B. Williams, and M. Rightley. Computer model calibration using high-dimensional output. Journal of the American Statistical Association, 103(482):570–583, 2008.

[49]

  N. J. Higham. The numerical stability of barycentric lagrange interpolation. IMA Journal of Numerical Analysis, 24(4):547–556, 2004.

[50]

  M. Hohenbichler and R. Rackwitz. Improvement of second-order reliability estimates by importance sampling. J. Eng. Mech., ASCE, 114(12):2195–2199, 1988.

[51]

  H.P. Hong. Simple approximations for improving second-order reliability estimates. J. Eng. Mech., ASCE, 125(5):592–595, 1999.

[52]

  R. L. Iman and W. J. Conover. A distribution-free approach to inducing rank correlation among input variables. Communications in Statistics: Simulation and Computation, B11(3):311–334, 1982.

[53]

  R. L. Iman and M. J Shortencarier. A Fortran 77 program and user's guide for the generation of latin hypercube samples for use with computer models. Technical Report NUREG/CR-3624, SAND83-2365, Sandia National Laboratories, Albuquerque, NM, 1984.

[54]

  D. Jones, M. Schonlau, and W. Welch. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13:455–492, 1998.

[55]

  M. C. Kennedy and A. O'Hagan. Bayesian calibration of computer models. Journal of the Royal Statistical Society, 63:425–464, 2001.

[56]

  W. A. Klimke. Uncertainty Modeling using Fuzzy Arithmetic and Sparse Grids. PhD thesis, Universität Stuttgart, Stuttgart, Germany, 2005.

[57]

  Computational investigations of low-discrepancy sequences. ACM Transactions on Mathematical Software, 23(2):266–294, 1997.

[58]

  Alexander Kraskov, Harald Stögbauer, and Peter Grassberger. Estimating mutual information. Physical review E, 69(6):066138, 2004.

[59]

  R. M. Lewis and S. N. Nash. A multigrid approach to the optimization of systems governed by differential equations. In Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, number AIAA-2000-4890, Long Beach, CA, Sep 2000.

[60]

  J. M. McFarland. Uncertainty Analysis for Computer Simulations through Validation and Calibration. PhD thesis, Vanderbilt University, Nashville, Tennesssee, 2008. available for download at http://etd.library.vanderbilt.edu/ETD-db/available/etd-03282008-125137/.

[61]

  M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239–245, 1979.

[62]

  J. C. Meza, R. A. Oliva, P. D. Hough, and P. J. Williams. OPT++: an object oriented toolkit for nonlinear optimization. ACM Transactions on Mathematical Software, 33(2), 2007.

[63]

  J. More and D. Thuente. Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software, 20(3):286–307, 1994.

[64]

  M. D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2):161–174, 1991.

[65]

  R. H. Myers and D. C. Montgomery. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons, Inc., New York, 1995.

[66]

  A. Nealen. A short-as-possible introduction to the least squares, weighted least squares, and moving least squares methods for scattered data approximation and interpolation. Technical report, Discrete Geometric Modeling Group, Technishe Universitaet, Berlin, Germany, 2004.

[67]

  J. Nocedal and Wright S. J. Numerical Optimization. Springer Series in Operations Research. Springer, New York, 1999.

[68]

  W.T. Nutt and G.B. Wallis. Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties. Reliability Engineering and System Safety, 83:57–77, 2004.

[69]

  W. .L. Oberkampf and J. C. Helton. Evidence theory for engineering applications. Technical Report SAND2003-3559P, Sandia National Laboratories, Albuquerque, NM, 2003.

[70]

  M. J. L. Orr. Introduction to radial basis function networks. Technical report, University of Edinburgh, Edinburgh, Scotland, 1996.

[71]

  V. M. Pérez, J. E. Renaud, and L. T. Watson. An interior-point sequential approximation optimization methodology. Structural and Multidisciplinary Optimization, 27(5):360–370, July 2004.

[72]

  T. D. Plantenga. HOPSPACK 2.0 user manual. Technical Report SAND2009-6265, Sandia National Laboratories, 2009.

[73]

  E. Prudencio and S. H. Cheung. Parallel adaptive multilevel sampling algorithms for the bayesian analysis of mathematical models. International Journal for Uncertainty Quantification, 2:215–237, 2012.

[74]

  D. G. Robinson and C. Atcitty. Comparison of quasi- and pseudo-monte carlo sampling for reliability and uncertainty analysis. In Proceedings of the AIAA Probabilistic Methods Conference, number AIAA99-1589, St. Louis, MO, 1999.

[75]

  M. Rosenblatt. Remarks on a multivariate transformation. Annals of Mathematical Statistics, 23(3):470–472, 1952.

[76]

  A. Saltelli, S. Tarantola, F. Campolongo, and M. Ratto. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models.. John Wiley & Sons, 2004.

[77]

  K. Schittkowski. NLPQLP: A fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search – user's guide. Technical report, Department of Mathematics, University of Bayreuth, Bayreuth, Germany, 2004.

[78]

  G. D. Sjaardema. APREPRO: An algebraic preprocessor for parameterizing finite element analyses. Technical Report SAND92-2291, Sandia National Laboratories, Albuquerque, NM, 1992.

[79]

  R. Srinivasan. Importance Sampling. Springer-Verlag, 2002.

[80]

  A. Stroud. Approximate Calculation of Multiple Integrals. Prentice Hall, 1971.

[81]

  L. P. Swiler and N. J. West. Importance sampling: Promises and limitations. In Proceedings of the 12th AIAA Non-Deterministic Approaches Conference, number AIAA-2010-2850, 2010.

[82]

  G. Tang, L. P. Swiler, and M. S Eldred. Using stochastic expansion methods in evidence theory for mixed aleatory-epistemic uncertainty quantification. In Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (12th AIAA Non-Deterministic Approaches conference), Orlando, FL, April 12-15, 2010. AIAA Paper 2010-XXXX.

[83]

  R. A. Tapia and M. Argaez. Global convergence of a primal-dual interior-point newton method for nonlinear programming using a modified augmented lagrangian function. (In Preparation).

[84]

  C. H. Tong. The PSUADE software library. Web site, 2005. http://www.llnl.gov/CASC/uncertainty_quantification/#psuade.

[85]

  Vanderplaats Research and Development, Inc., Colorado Springs, CO. DOT Users Manual, Version 4.20, 1995.

[86]

  R. J. Vanderbei and D. F. Shanno. An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications, 13:231–259, 1999.

[87]

  G. N. Vanderplaats. CONMIN – a FORTRAN program for constrained function minimization. Technical Report TM X-62282, NASA, 1973. See also Addendum to Technical Memorandum, 1978.

[88]

  G. N. Vanderplaats. Numerical Optimization Techniques for Engineering Design: With Applications. McGraw-Hill, New York, 1984.

[89]

  J. A. Vrugt, C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman, and D. Higdon. Accelerating Markov chain Monte Carlo simulation by self-adaptive differential evolution with randomized subspace sampling. International Journal of Nonlinear Scientific Numerical Simulation, 10(3), 2009.

[90]

  V. G. Weirs, J. R. Kamm, L. P. Swiler, M. Ratto, S. Tarantola, B. M. Adams, W. J. Rider, and M. S Eldred. Sensitivity analysis techniques applied to a system of hyperbolic conservation laws. Reliability Engineering and System Safety, 107:157–170, 2012.

[91]

  S. S. Wilks. Determination of sample sizes for setting tolerance limits. Ann. Math. Stat., 12(1):91–96, 1941.

[92]

  S. J. Wright. Primal-Dual Interior-Point Methods. SIAM, 1997.

[93]

  G. D. Wyss and K. H. Jorgensen. A user's guide to LHS: Sandia's Latin hypercube sampling software. Technical Report SAND98-0210, Sandia National Laboratories, Albuquerque, NM, 1998.

[94]

  D. Xiu. Numerical integration formulas of degree two. Applied Numerical Mathematics, 58:1515–1520, 2008.

[95]

  S. Xu and R. V. Grandhi. Effective two-point function approximation for design optimization. AIAA J., 36(12):2269–2275, 1998.

[96]

  D. C. Zimmerman. Genetic algorithms for navigating expensive and complex design spaces, September 1996. Final Report for Sandia National Laboratories contract AO-7736 CA 02.