A DOPED DERIVATIVE-FREE ALGORITHM

R. Oeuvray∗ and M. Bierlaire∗∗

References

  1. [1] J.E. Dennis & R.B. Schnabel, Numerical methods for un-constrained optimization and nonlinear equations (EnglewoodCliffs, USA: Prentice-Hall, 1983).
  2. [2] D.P. Bertsekas, Nonlinear programming (Athena Scientific,Belmont, 1995).
  3. [3] R. Oeuvray. Trust-Region Methods Based on Radial BasisFunctions with Application to Biomedical Imaging, Ph.D.thesis, Ecole Polytechnique F´ed´erale de Lausanne, 2005.
  4. [4] R. Oeuvray & M. Bierlaire, BOOSTERS: A derivative-freealgorithm based on radial basis functions, International Journalof Modelling and Simulation, to appear.
  5. [5] R.M. Lewis, V. Torczon, & M.W. Trosset, Direct searchmethods: Then and now, Journal of Computational andApplied Mathematics, 124, 2000, 191–207.
  6. [6] R. Hooke & T.A. Jeeves, Direct search solution of numericaland statistical problems, Journal of the ACM, 8, 1961, 212–229.
  7. [7] V. Torczon, On the convergence of pattern search algorithms,SIAM Journal on Optimization, 7(1), 1997, 1–25.
  8. [8] W. Spendley, G.R. Hext, & F.R. Himsworth, Sequential ap-plication of simplex designs in optimization and evolutionaryoperation, Technometrics, 4, 1962.
  9. [9] J.A. Nelder & R. Mead, A simplex method for functionminimization, Computer Journal, 7, 1965, 308–313.
  10. [10] K.I. McKinnon, Convergence of the Nelder-Mead simplexmethod to a nonstationary point, SIOPT, 9(1), 1998, 148–158.
  11. [11] H.H. Rosenbrock, An automatic method for finding the greatestor least value of a function, The Computer Journal, 3, 1960,175–184.
  12. [12] M.J.D. Powell, An efficient method for finding the minimum ofa function of several variables without calculating derivatives,Computer Journal, 17, 1964, 155–162.
  13. [13] A.R. Conn & Ph.L. Toint, An algorithm using quadratic in-terpolation for unconstrained derivative free optimization, inG. Di Pillo & F. Gianessi (Eds.), Nonlinear optimization andapplications (Plenum Publishing, 1996), 27–47. Also avail-able as Report 95/6, Dept of Mathematics, FUNDP, Namur,Belgium.
  14. [14] M.J.D. Powell, UOBYQA: unconstrained optimization byquadratic approximation, Technical Report DAMTP NA14,Department of Applied Mathematics and Theoretical Physics,Cambridge University, Cambridge, UK, 2000.
  15. [15] M.J.D. Powell, On the use of quadratic models in unconstrainedminimization without derivatives, Technical Report DAMTPNA03, Department of Applied Mathematics and TheoreticalPhysics, Cambridge University, Cambridge CB3 9EW, UK,2003.
  16. [16] A.J. Booker, J.E. Dennis, P.D. Frank, D.B. Serafini, V. Torc-zon, & M.W. Trosset, A rigourous framework for optimization392of expensive functions by surrogates, Technical report, Mathe-matics & Engineering Analysis, Boeing Shared Services Group,1998.
  17. [17] A.R. Conn, N.I.M. Gould, & Ph. Toint, Trust region methods,MPS–SIAM Series on Optimization, SIAM, 2000.
  18. [18] M. Bierlaire, BIOGEME: a free package for the estimation ofdiscrete choice models, Proc. of the 3rd Swiss TransportationRes. Conf., Ascona, Switzerland, 2003, www.strc.ch.
  19. [19] M. Bierlaire, An introduction to BIOGEME version 1.4. bio-geme.epfl.ch, 2005.
  20. [20] C.T. Lawrence, J.L. Zhou & A. Tits, User’s guide for CFSQPversion 2.5: A C code for solving (large scale) constrainednonlinear (minimax) optimization problems, generating iteratessatisfying all inequality constraints, Technical Report TR-94-16r1, Institute for Systems Research, University of Maryland,College Park, MD 20742, 1997, 1997.

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