Mesh adaptive direct search algorithms for constrained optimization

SIAM Journal on Optimization

Volumn 17, Issue 1, 2007, Pages 188-217

  Audet, Charles ^a   Dennis Jr , J E ^b  

^a GERAD   (Canada)

^b Rice University   (United States)

Author keywords

Clarke derivatives; Constrained optimization; Contingent cone; Convergence analysis; Hypertangent; Mesh adaptive direct search algorithms (MADS); Nonsmooth analysis

Indexed keywords

CLARKE DERIVATIVES; CONSTRAINED OPTIMIZATION; CONTINGENT CONE; CONVERGENCE ANALYSIS; HYPERTANGENT; MESH ADAPTIVE DIRECT SEARCH ALGORITHMS (MADS); NONSMOOTH ANALYSIS;

COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; PROBLEM SOLVING;

ADAPTIVE ALGORITHMS;

EID: 33750265086     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/040603371     Document Type: Article

References (32)

1. M. A. ABRAMSON, C. AUDET, AND J. E. DENNIS, JR., Generalized pattern searches with derivative information, Math. Program., 100 (2004), pp. 3-25.
2. C. AUDET, Convergence results for pattern search algorithms are tight, Optim. Eng., 5 (2004), pp. 101-122.
3. C. AUDET AND J. E. DENNIS, JR., Analysis of generalized pattern searches, SIAM J. Optim., 13 (2003), pp. 889-903.
4. C. AUDET AND J. E. DENNIS, JR., A pattern search filter method for nonlinear programming without derivatives, SIAM J. Optim., 14 (2004), pp. 980-1010.
5. C. AUDET AND D. ORBAN, Finding optimal algorithmic parameters using the mesh adaptive direct search algorithm, SIAM J. Optim., to appear.
6. M. AVRIEL, Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, NJ, 1976.
7. V. BÉCHARD, C. AUDET, AND J. CHAOUKI, Robust optimization of chemical processes using a mads algorithm, Technical report G-2005-16, Les Cahiers du Gerad, Montreal, Canada, 2005.
8. A. J. BOOKER, J. E. DENNIS, JR., P. D. FRANK, D. B. SERAFINI, V. TORCZON, AND M. W. TROSSET, A rigorous framework for optimization of expensive functions by surrogates, Structural Optim., 17 (1999), pp. 1-13.
9. T. D. CHOI AND C. T. KELLEY, Superlinear convergence and implicit filtering, SIAM J. Optim., 10 (2000), pp. 1149-1162.
10. F. H. CLARKE, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. Reissued in 1990 by SIAM Publications, Philadelphia, as Vol. 5 in the series Classics in Applied Mathematics.
11. I. D. COOPE AND C. J. PRICE, Frame based methods for unconstrained optimization, J. Optim. Theory Appl., 107 (2000), pp. 261-274.
12. I. D. COOPE AND C. J. PRICE, On the convergence of grid-based methods for unconstrained optimization, SIAM J. Optim., 11 (2001), pp. 859-869.
13. G. COUTURE, C. AUDET, J. E. DENNIS, JR., AND M. A. ABRAMSON, The NOMAD project, http://www.gerad.ca/ NOMAD/.
14. C. DAVIS, Theory of positive linear dependence, Amer. J. Math., 76 (1954), pp. 733-746.
15. D. E. FINKEL AND C. T. KELLEY, Convergence analysis of the direct algorithm, Technical report, NCSU Mathematics Department, Raleigh, NC, 2004.
16. F. J. GOULD AND J. W. TOLLE, Geometry of optimality conditions and constraint qualifications, Math. Program., 2 (1972), pp. 1-18.
17. R. E. HAYES, F. H. BERTRAND, C. AUDET, AND S. T. KOLACZKOWSKI, Catalytic combustion kinetics: Using a direct search algorithm to evaluate kinetic parameters from light-off curves, The Canadian Journal of Chemical Engineering, 81 (2003), pp. 1192-1199.
18. J. JAHN, Introduction to the Theory of Nonlinear Optimization, Springer-Verlag, Berlin, 1996.
19. T. G. KOLDA, R. M. LEWIS, AND V. TORCZON, Optimization by direct search: new perspectives on some classical and modern methods, SIAM Rev., 45 (2003), pp. 385-482.
20. E. B. LEACH, A note on inverse function theorems, Proc. Amer. Math. Soc., 12 (1961), pp. 694-697.
21. R. M. LEWIS AND V. TORCZON, Rank ordering and positive bases in pattern search algorithms, Technical report 96-71, Institute for Computer Applications in Science and Engineering, Mail Stop 132C, NASA Langley Research Center, Hampton, VA, 1996.
22. R. M. LEWIS AND V. TORCZON, A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds, SIAM J. Optim., 12 (2002), pp. 1075-1089.
23. S. LUCIDI, M. SCIANDRONE, AND P. TSENG, Objective-derivative-free methods for constrained optimization, Math. Program., 92 (2002), pp. 37-59.
24. A. L. MARSDEN, Aerodynamic Noise Control by Optimal Shape Design, Ph.D. thesis, Stanford University, Stanford, CA, 2004.
25. Mathworks. Matlab gads toolbox. http://www.mathworks.com/products/gads/.
26. C. J. PRICE AND I. D. COOPE, Frames and grids in unconstrained and linearly constrained optimization: a nonsmooth approach, SIAM J. Optim., 14 (2003), pp. 415-438.
27. C. J. PRICE, I. D. COOPE, AND J. E. DENNIS, JR., Direct search methods for nonlinearly constrained optimization using filters and frames, Optim. Eng., 5 (2004), pp. 123-144.
28. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
29. R. T. ROCKAFELLAR, Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math., 32 (1980), pp. 257-280.
30. V. TORCZON, On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 1-25.
31. Z. B. ZABINSKY AND R. L. SMITH, Pure adaptive search in global optimization, Math. Program., 53 (1992), pp. 323-338.
32. Z. B. ZABINSKY, Stochastic Adaptive Search for Global Optimization, Nonconvex Optimization and its Applications, 72, Kluwer Academic Publishers, Boston, 2003.