A surrogate management framework using rigorous trust-region steps

Optimization Methods and Software

Volumn 29, Issue 1, 2014, Pages 10-23

  Gratton, S ^a   Vicente, L N ^b  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

global convergence; search step; Surrogate modelling; trust region methods

Indexed keywords

DERIVATIVE-FREE OPTIMIZATION; ENGINEERING COMMUNITY; GLOBAL CONVER-GENCE; MANAGEMENT FRAMEWORKS; SEARCH STEPS; SURROGATE MODELLING; TRUST-REGION ALGORITHMS; TRUST-REGION METHODS;

ALGORITHMS; FUEL ADDITIVES; IMAGE REGISTRATION;

COMPUTER SIMULATION;

EID: 84887534277     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2012.719508     Document Type: Article

References (22)

1. C. Audet and D. Orban, Finding optimal algorithmic parameters using derivative-free optimization, SIAM J. Optim. 17 (2006), pp. 642-664
2. C. Audet, J.E. Dennis, and S. Le Digabel, Globalization strategies for mesh adaptive direct search, Comput. Optim. Appl. 46 (2010), pp. 193-215
3. A.S. Bandeira, K. Scheinberg, and L.N. Vicente, Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization, Math. Program. 134 (2012), pp. 223-257
4. 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. Struct. Multidisc. Optim. 17 (1998), pp. 1-13
5. A.R. Conn, N.I.M. Gould, and Ph.L. Toint, Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2000
6. A.R. Conn, K. Scheinberg, and L.N.Vicente, Global convergence of general derivative-free trust-region algorithms to first and second order critical points, SIAM J. Optim. 20 (2009), pp. 387-415
7. A.R. Conn, K. Scheinberg, and L.N. Vicente. Introduction to Derivative-Free Optimization, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2009
8. A.L. Custódio, H. Rocha, and L.N. Vicente, Incorporating minimum Frobenius norm models in direct search, Comput. Optim. Appl. 46 (2010), pp. 265-278
9. G. Fasano, J.L. Morales, and J. Nocedal, On the geometry phase in model-based algorithms for derivative-free optimization, Optim. Meth. Softw. 24 (2009), pp. 145-154
10. A.J. Keane and P. Nair, Computational Approaches for Aerospace Design: The Pursuit of Excellence, JohnWiley & Sons, NewYork, 2006
11. 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
12. A.L. Marsden, M. Wang, J.E. Dennis Jr., and P. Moin, Optimal aeroacoustic shape design using the surrogate management framework, Optim. Eng. 5 (2004), pp. 235-262
13. J.J. Moré and D.C. Sorensen, Computing a trust region step, SIAM J. Sci. Comput. 4 (1983), pp. 553-572
14. J.J. Moré and S.M. Wild, Benchmarking derivative-free optimization algorithms, SIAM J. Optim. 20 (2009), pp. 172-191
15. G. Nicosia and G. Stracquadanio, Generalized pattern search algorithm for peptide structure, Biophys. J. 95 (2008), pp. 4988-4999
16. K. Scheinberg and L. Toint, Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization, SIAM J. Optim. 20 (2010), pp. 3512-3532
17. D.B. Serafini, A framework for managing models in nonlinear optimization of computationally expensive functions, Ph.D thesis, Department of Computational and Applied Mathematics, Rice University, 1998
18. J. Søndergaard, Optimization using surrogate models-by the space mapping technique, Ph.D thesis, Informatics and Mathematical Modelling, Technical University of Denmark, 2003
19. V. Torczon and M.W. Trosset, Using Approximations to Accelerate Engineering Design Optimization, Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, Missouri, September 2-4, 1998
20. A.I.F. Vaz and L.N. Vicente, A particle swarm pattern search method for bound constrained global optimization, J. Global Optim. 39 (2007), pp. 197-219
21. T. Zhang, K.K. Choi, S. Rahman, K. Cho, P. Baker, M. Shakil, and D. Heitkamp, A hybrid surrogate and pattern search optimization method and application to microelectronics, Struct. Multidisc. Optim. 32 (2006), pp. 327-345
22. H. Zhang, A.R. Conn, and K. Scheinberg, A derivative-free algorithm for least-squares minimization, SIAM J. Optim. 20 (2010), pp. 3555-3576