On sensitivity analysis for problems with numerical noise

9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

Volumn , Issue , 2002, Pages

  Borggaard, J ^a   Pelletier, D ^b   Vugrin, K ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

SENSITIVITY ANALYSIS;

GRADIENT INFORMATIONS; NAVIER STOKES; NUMERICAL NOISE; OBJECTIVE FUNCTIONS; OPTIMAL DESIGN; OPTIMIZATION PROBLEMS; SENSITIVITY EQUATIONS;

NAVIER STOKES EQUATIONS;

EID: 85087191273     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2002-5553     Document Type: Conference Paper

References (21)

1. A. A. Giunta, V. Balbanov, D. Haim, B. Grossman, W. H. Mason, L. T. Watson, and R. T. Haftka. Multidisciplinary optimisation of a supersonic transport using design of experiments theory and response surface modellling. Aeronautical Journal, 101(1008):347-356, 1997.
2. M. Schonlau, W. J. Welch, and D. R. Jones. Global versus local search in constrained optimization of computer models. In New developments and applications in experimental design, IMS Lecture Notes-Monograph Series 34, pages 11-25, 1997.
3. N. Alexandrov, J. E. Dennis, Jr., R. M. Lewis, and V. Torczon. A trust-region framework for managing the use of approximation models in optimization. Technical Report ICASE Report No. 97-50, NASA, Langley Research Center, Hampton VA 23681-0001, 1997.
4. M. S. Gockenbach and W. W. Symes. Adaptive simulation, the adjoint state method, and optimization. In Proc. First Sandia Workshop on Large-Scale PDE-Constrained Optimization. to appear.
5. J. T. Betts, N. Biehn, S. L. Campbell, and W. P. Hufiman. Compensating for order variation in mesh refinement for direct transcription methods. J. Comput. Appl. Math., 125:147-158, 2000.
6. J. Borggaard. On the presence of shocks in domain optimization of Euler ows. In M. Gunzburger, editor, Flow Control, volume 68 of Proceedings of the IMA. Springer- Verlag, 1995.
7. R. Narducci, B. Grossman, and R. Haftka. Design sensitivity algorithms for an inverse design problem involving a shock wave. Inverse Problems in Engineering, 2:49-83, 1995.
8. R. Narducci, B. Grossman, M. Valorani, A. Dadone, and R. T. Haftka. Optimization methods for non-smooth or noisy objective functions in uid design problems. In Proc. AIAA 12th Computational Fluid Dynamics Conference, June 1995.
9. M. Kaufman, V. Balabanov, S. L. Burgee, A. A. Giunta, B. Grossman, R. T. Haftka, W. H. Mason, and L. T. Watson. Variable-complexity response surface approximations for wing structural weight in hsct design. Computational Mechanics, 18(2):112-126, 1996.
10. P. Gilmore, C. T. Kelley, C. T. Miller, and G. A. Williams. Implicit filtering and optimal design problems. In J. Borggaard, J. Burkardt, M. Gunzburger, and J. Peterson, editors, Optimal Design and Control, pages 97-116. Birkhauser, 1995.
11. V. Torczon. On the convergence of the multidirectional search algorithm. SIAM J. Optim., 1(1):123-145, 1991.
12. A. Conn, K. Scheinberg, and P. Toint. On the convergence of derivative-free methods for unconstrained optimization. In M. D. Buhmann and A. Iserles, editors, Approximation Theory and Optimization, pages 83-108. Cambridge University Press, 1997.
13. D. M. Bortz and C. T. Kelley. The simplex gradient and noisy optimization problems. In J. Borggaard, J. Burns, E. Clifi, and S. Schreck, editors, Computational Methods for Optimal Design and Control, pages 77-90. Birkhäuser, 1998.
14. J. Borggaard, J. Burns, E. Clifi, and M. Gunzburger. Sensitivity calculations for a 2D, inviscid, supersonic forebody problem. In H. T. Banks, R. Fabiano, and K. Ito, editors, Identification and Control of Systems Governed by Partial Difierential Equations, pages 14-24, Philadelphia, PA, 1993. SIAM Publications.
15. R. G. Carter. On the global convergence of trust-region algorithms using inexact gradient information. SIAM J. Numer. Anal., 28(1):251-265, 1991.
16. J. Borggaard and J. Burns. Asymptotically consistent gradients in optimal design. In N. Alexandrov and M. Hussaini, editors, Multidisciplinary Design Optimization: State of the Art, pages 303-314, Philadelphia, PA, 1997. SIAM Publications.
17. J. Borggaard and A. Verma. On eficient solutions to the continuous sensitivity equation using automatic difierentiation. SIAM J. Sci. Comput., 22(1):39-62, 2001.
18. A. Griewank and G. F. Corliss, editors. Automatic Difierentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, PA, 1991.
19. J. Burkardt, M. Gunzburger, and J. Peterson. Insensitive functionals, inconsistent gradients, spurious minima, and regularized functionals in flow optimization problems. International Journal on Computational Fluid Dynamics, 16(3):171-185, 2002.
20. th AIAA Aerospace Sciences Meeting and Exhibit, 1998. AIAA Paper 98-0908.
21. J. Borggaard and J. Burns. A PDE sensitivity equation method for optimal aerodynamic design. J. Comput. Phys., 136(2):366-384, 1997.