Abstract
We discuss first-order approximation and model management optimization, an approach to the optimization of systems governed by differential equations. Our approach tries to alleviate the expense of relying exclusively on high-fidelity simulations, e.g., the solution of the governing differential equations on very fine meshes or the use of very detailed physics, while still guaranteeing global convergence of the overall optimization process to a solution of the high-fidelity problem. We focus here on several model management methods and experience with their performance.
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References
N. M. Alexandrov, On managing the use of surrogates in geneml nonlinear optimization, September 1998. AIAA Paper 98-4798.
N. M. Alexandrov and R. M. Lewis, A trust region framework for managing approximation models in engineering optimization, September 1996. AIAA Papers 96-4101 and 96-4102.
-, Algorithmic perspectives on problem formulations in MDO. AIAA Paper 2000-4719, 2000.
-, Analytical and computational properties of distributed approaches to MDO. AIAA Paper 2000-4718, September 2000.
N. M. Alexandrov, R. M. Lewis, C. R. Gumbert, L. L. Green, and P. A. Newman, Optimization with variable-fidelity models applied to wing design. AIAA Paper 2000-0841, January 2000. Accepted for publication in the AIAA Journal of Aircraft.
N. M. Alexandrov, E. J. Nielsen, R. M. Lewis, and W. K. Anderson, First-order model management with variable-fidelity physics applied to multielement airfoil optimization. AIAA Paper 2000-4886, September 2000.
W. K. Anderson and D. L. Bonhaus, An implicit upwind algorithm for computing turbulent flows on unstructured grids, Computers and Fluids, 23 (1994), pp. 1–21.
-, Aerodynamic design on unstructured grids for turbulent flows, Tech. Rep. NASA TM 112867, NASA Langley Res earch Center, June 1997.
J.-F. M. Barthelemy and R. T. Haftka, Approximation concepts for optimum structural design—a review, Structural Optimization, 5 (1993), pp. 129–144.
S. Burgee, A. Giunta, V. Balabanov, B. Grossman, W. Mason, R. Narducci, R. Haftka, and L. Watson, A coarse-gmined parallel variablecomplexity multidisciplinary optimization problem, The International Journal of Supercomputing Applications and High Performance Computing, 10 (1996), pp. 269–299.
K. J. Chang, R. T. Haftka, G. L. Giles, and P.-J. Kao, Sensitivity-based scaling for approximating structural response, Journal of Aircraft, 30 (1993), pp. 283–288.
A. R. Conn, N. Gould, and P. L. Toint, LANCELOT: a Fortran package for large-scale nonlinear optimization (release A), vol. 17 of Springer series in computational mathematics, Springer-Verlag, New York, 1992.
-, Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM-MPS, Philadelphia, 2000.
A. R. Conn, N. I. M. Gould, and P. L. Toint, A globally convergent augmented Lagmngian algorithm for optimization with geneml constmints and simple bounds, SIAM Journal on Numerical Analysis, 28 (1991), pp. 545–572.
R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, Chichester, 1989. Second Edition.
P. E. Gill, G. H. Golub, W. Murray, and M. H. Wright, User’s guide for SOL/NPSOL: a Fortran package for nonlinear programming, Department of Operations Research, Stanford University, Stanford, CA, 1983.
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, Academic Press, London, 1981.
A. Giunta, Aircraft Multidisciplinary Optimization Using Design of Experiments Theory and Response Surface Modeling Methods, PhD thesis, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA, 1997.
R. T. Haftka, Combining global and local approximations, AIAA Journal, 29 (1991), pp. 1523–1525.
R. T. Haftka, Z. Gürdal, and M. P. Kamat, Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht, 1990.
L. Kaufman and D. Gay, PORT Library: Optimization and Mathematical Programming, Bell Laboratories, May 1997.
R. M. Lewis and S. G. Nash, A multigrid approach to the optimization of systems governed by differential equations. AIAA Paper 2000-4890, 2000.
J. C. Newman, III, A. C. Taylor, III, R. W. Barnwell, P. A. Newman, and G. J.-W. Hou, Overview of sensit ivity analysis and shape optimization for complex aerodynamic configurations, Journal of Aircraft, 36 (1999), pp. 87–96.
M. Powell, Converyence properties of a class of minimization algorithms, in Nonlinear Programming 2, O. Mangasarian, R. Meyer, and S. Robinson, eds., Academic Press, New York, NY, 1975, pp. 1–27.
M. J. D. Powell, Variable metric methods for constrained optimization, in Mathematical Programming, the State of the Art, A. Bachem, M. Grotschel, and B. Korte, eds., Springer-Verlag, 1983, pp. 288–311.
J. RodrÃguez, J. Renaud, and L. Watson, Trust region augmented Lagrangian methods for sequential response surface approximation and optimization, in Proceedings of DETC’ 97, September 1997. ASME paper DETC97DAC3773, presented at the 1997 ASME Design Engineering Technical Conferences, September 14–17, Sacramento, California.
J.-Y. Trepanier. Personal communication, 2001.
R. T. Whitcomb and L. R. Clark, An airfoil shape for efficient flight at supercritical mach numbers, Tech. Rep. NASA TM-X-ll09, NASA Langley Research Center, 1965.
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Alexandrov, N.M., Lewis, R.M. (2003). First-Order Approximation and Model Management in Optimization. In: Biegler, L.T., Heinkenschloss, M., Ghattas, O., van Bloemen Waanders, B. (eds) Large-Scale PDE-Constrained Optimization. Lecture Notes in Computational Science and Engineering, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55508-4_4
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DOI: https://doi.org/10.1007/978-3-642-55508-4_4
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