CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm

Journal of Computational and Applied Mathematics

Volumn 181, Issue 1, 2005, Pages 157-175

  Vanden Berghen, Frank ^a   Bersini, Hugues ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

High computing load; Lagrange interpolation; Noisy optimization; Nonlinear; Optimal shape design; Parallel computing; Trust region method

Indexed keywords

APPROXIMATION THEORY; C (PROGRAMMING LANGUAGE); COMPUTATIONAL FLUID DYNAMICS; INTERPOLATION; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; OBJECT ORIENTED PROGRAMMING; OPTIMIZATION; PARALLEL ALGORITHMS; PARTIAL DIFFERENTIAL EQUATIONS;

HIGH COMPUTING LOAD; LAGRANGE INTERPOLATION; NOISY OPTIMIZATION; OPTIMAL SHAPE DESIGN; TRUST REGION METHOD;

PARALLEL PROCESSING SYSTEMS;

EID: 19444379764     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.11.029     Document Type: Article

References (44)

1. Aemdesign, URL: http://www.aemdesign.com/FSQPapplref.htm.
2. P.T. Boggs, J.W. Tolle, Sequential quadratic programming, Acta Numer. (1996) 1-000.
3. A.J. Booker, A.R. Conn, J.E. Dennis Jr., P.D. Frank, M. Trosset, V. Torczon, M.W. Trosset, Global modeling for optimization: Boeing/ibm/rice collaborative project 1995 Final Report, Technical Report ISSTECH-95-032, Boeing Information Support Services, Research and Technology, Box 3707, M/S 7L-68, Seattle, WA 98124, December 1995.
4. A.J. Booker, J.E. Dennis Jr., P.D. Frank, D.B. Serafini, V. Torczon, M.W. Trosset, Optimization using surrogate objectives on a helicopter test example, Comput. Methods Optimal Design Control (1998) 49-58.
5. D.M. Bortz, C.T. Kelley, The simplex gradient and noisy optimization problems, Technical Report CRSC-TR97-27, North Carolina State University, Department of Mathematics, Center for Research in Scientific Computation, Box 8205, Raleigh, NC 27695-8205, September 1997.
6. R.G. Carter J.M. Gablonsky A. Patrick C.T. Kelley O.J. Eslinger Algorithms for noisy problems in gas transmission pipeline optimization Optim. Eng. 2 2001 139-157
7. A.R. Conn, N.I.M. Gould, P.L. Toint, LANCELOT: A Fortran Package for Large-scale Non-linear Optimization (Release A), Springer Series in Computational Mathematics ed., Springer, HeidelBerg, Berlin, New York, 1992.
8. A.R. Conn, N.I.M. Gould, P.L. Toint, A derivative free optimization algorithm in practice, Technical Report, Report No. 98/11, Department of Mathematics, University of Namur, Belgium, 1998.
9. A. R. Conn, N.I.M. Gould, P.L. Toint, Trust-region Methods, MPS-SIAM Series on Optimization ed., SIAM Society for Industrial & Applied Mathematics, Englewood Cliffs, NJ, 2000, pp. 307-323 (Chapter 9: conditional model).
10. A.R. Conn, N.I.M. Gould, P.L. Toint, The ideal trust region, in: Trust-region Methods, MPS-SIAM Series on Optimization ed., SIAM Society for Industrial & Applied Mathematics, Englewood Cliffs, NJ, 2000, pp. 236-237.
11. A.R. Conn, N.I.M. Gould, P.L. Toint, Note on convex models, in: Trust-region Methods, MPS-SIAM Series on Optimization ed., SIAM Society for Industrial & Applied Mathematics, Englewood Cliffs, NJ, 2000, pp. 324-337.
12. A.R. Conn K. Scheinberg P.L. Toint Recent progress in unconstrained nonlinear optimization without derivatives Math. Programming 79 1997 397-414
13. R. Cosentino Z. Alsalihi R. Van Den Braembussche Expert system for radial impeller optimisation Proceedings of the Fourth European Conference on Turbomachinery ATI-CST-039/01, Florence, Italy 2001
14. C. De Boor A.A. Ron On multivariate polynomial interpolation Constr. Approx. 6 1990 287-302
15. J.E. Dennis Jr., R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics, 16 ed., SIAM Society for Industrial & Applied Mathematics, Englewood Cliffs, NJ, 1996.
16. J.E. Dennis Jr. V. Torczon Direct search methods on parallel machines SIAM J. Optim. 1 4 1991 448-474
17. J.E. Dennis Jr. H.F. Welaker Inaccurracy in quasi-Newton methods: Local improvement theorems Math. Programming Stud. 22 1984 70-85
18. R. Fletcher Practical Methods of Optimization 1987 Wiley-Interscience Great Britain
19. R. Fourer D.M. Gay B.W. Kernighan AMPL: A Modeling Language for Mathematical Programming 2002 Duxbury Press/Brooks/Cole Publishing Company
20. P.E. Gill, W. Murray, M.A. Saunders, M.H. Wright, Users's guide for npsol (version 4.0): A fortran package for non-linear programming, Technical Report, Report SOL 862, Department of Operations Research, Stanford University, Stanford, CA 94305, USA, 1986.
21. P. Gilmore C.T. Kelley An implicit filtering algorithm for optimization of functions with many local minima SIAM J. Optim. 5 1995 269-285
22. G.H. Golub C.F. Van Loan Matrix Computations third ed. 1996 Johns Hopkins University Press Baltimore, USA
23. N.I.M. Gould, D. Orban, P.L. Toint, CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited, Technical Report, Report No. TR/PA/01/04, Cerfacs, 2001.
24. W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, vol. 187, 1981.
25. C.T. Kelley, Iterative Methods for Optimization, vol. 18, Frontiers in Applied Mathematics, 1999.
26. C.L. Lawson R.J. Hanson D. Kincaid F.T. Krogh Basic linear algebra subprograms for FORTRAN usage ACM Trans. Math. Soft. 5 1979 308-323
27. J.J. Moré D.C. Sorensen Computing a trust region step SIAM J. Sci. Statist. Comput. 4 3 1983 553-572
28. E.R. Panier A.L. Tits On combining feasibility, descent and superlinear convergence in inequality contrained optimization Math. Programming 59 1995 261-276
29. S. Pazzi F. Martelli V. Michelassi F.V. Berghen H. Bersini Intelligent performance CFD optimisation of a centrifugal impeller Proceedings of the Fifth European Conference on Turbomachinery Prague, CZ March 2003
30. S. Pierret, R. Van den Braembussche, Turbomachinery blade design using a Navier-Stokes solver and artificial neural network, J. Turbomach. ASME 98-GT-4 (1998) (publication in the transactions of the ASME: J. Turbomach.).
31. V. Pediroda, M. Poian, C. Poloni, Multi objective optimisation examples: Design of a laminar airfoil and of a composite rectangular wing, in: Genetic Algorithms for Optimisation in Aeronautics and Turbomachinery, von Karman Institute Lecture Series Monographs 200-07, 2000.
32. M.J.D. Powell, A direct search optimization method that models the objective and constraint functions by linar interpolation, in: S. Gomez, J.-P. Hennart (Eds.), Advances in Optimization and Numerical Analysis, Proceedings of the Sixth Workshop on Optimization and Numerical Analysis, Oaxaca, Mexico, vol. 275, Kluwer Academic Publishers, Dordrecht, NL, 1994, pp. 51-67.
33. M.J.D. Powell. The use of band matrices for second derivative approximations in trust region algorithms, Technical Report No. DAMTP1997/NA12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 1997.
34. M.J.D. Powell, On the Lagrange function of quadratic models that are defined by interpolation, Technical Report No. DAMTP2000/10, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 2000.
35. M.J.D. Powell, UOBYQA: Unconstrained optimization by quadratic approximation, Technical Report No. DAMTP2000/14, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 2000.
36. M.J.D. Powell UOBYQA: Unconstrained optimization by quadratic approximation Math. Programming B 92 2002 555-582
37. M.J.D. Powell, On updating the inverse of a KKT matrix, Technical Report No. DAMTP2004/01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England, 2004.
38. T. Sauer Y. Xu On multivariate lagrange interpolation Math. Comp. 64 1995 1147-1170
39. D.E. Stoneking G.L. Bilbro R.J. Trew P. Gilmore C.T. Kelley Yield optimization using a GaAs process simulator coupled to a physical device model IEEE Trans. Microwave Theory Tech. 40 1992 1353-1363
40. F. Vanden Berghen, Intermediate report on the development of an optimization code for smooth, continuous objective functions when derivatives are not available, Technical Report, IRIDIA, Université Libre de Bruxelles, Belgium.
41. F. Vanden Berghen, Optimization algorithm for non-linear, constrained, derivative-free optimization of continuous, high-computing-load functions, Technical Report, IRIDIA, Université Libre de Bruxelles, Belgium, available at http://iridia.ulb.ac.be/~fvandenb/ mythesis/, 2004.
42. J.F. Wanga J. Periaux M. Sefriouib Parallel evolutionary algorithms for optimization problems in aerospace engineering J. Comput. Appl. Math. 149 1 2002 155-169
43. D. Winfield, Function and functional optimization by interpolation in data tables, Ph.D. Thesis, Harvard University, Cambridge, USA, 1969.
44. D. Winfield Function minimization by interpolation in a data table J. Inst. Math. Appl. 12 1973 339-347