R. Oeuvray∗ and M. Bierlaire∗∗
[1] R.M. Lewis, V. Torczon, & M.W. Trosset, Direct searchmethods: Then and now, Journal of Computational andApplied Mathematics, 124, 2000, 191–207. [2] V. Torczon, On the convergence of pattern search algorithms,SIAM Journal on Optimization, 7(1), 1997, 1–25. [3] J.A. Nelder & R. Mead, A simplex method for functionminimization, Computer Journal, 7, 1965, 308–313. [4] H.H. Rosenbrock, An automatic method for finding the greatestor least value of a function, The Computer Journal, 3, 1960,175–184. [5] 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. [6] A.R. Conn & Ph.L. Toint, An algorithm using quadraticinterpolation for unconstrained derivative free optimization, inG. Di Pillo & F. Gianessi (Eds.) Nonlinear optimization andapplications (New York: Plenum Publishing, 1996), 27–47.Also available as Report 95/6, Department of Mathematics,FUNDP, Namur, Belgium. [7] 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. [8] M.J.D. Powell, The NEWUOA software for unconstrainedoptimization without derivatives. Technical Report DAMTPNA2004/08, Department of Applied Mathematics and Theo-retical Physics, Cambridge University, Cambridge CB3 9EW,UK, 2004. [9] A.J. Booker, J.E. Dennis, P.D. Frank, D.B. Serafini, V. Torc-zon, & M.W Trosset, A rigourous framework for optimizationof expensive functions by surrogates, Structural Optimization,17(1): 1999, 1–13. [10] R. Oeuvray, Trust-region methods based on radial basis func-tions with application to biomedical imaging, Ph.D. Thesis,Ecole Polytechnique F´ed´erale de Lausanne, 2005. [11] N.I.M. Gould, D. Orban, & Ph.L. Toint, General CUTErdocumentation. Technical Report TR/PA/02/13, CERFACS,2002. [12] A.R. Conn, N.I.M. Gould, & Ph. Toint, Trust region methods,MPS–SIAM Series on Optimization, SIAM, 2000. [13] J. Duchon, Splines minimizing rotation-invariant semi-normsin Sobolev spaces, Constructive theory of functions of severalvariables (Springer, 1977), 85–100. [14] M.D. Buhmann, Multivariate approximation and applications,chapter Approximation and interpolation with radial functions(Cambridge, 2001), 25–43. [15] R.L. Hardy, Computers and mathematics with applications,Vol. 19, chapter Theory and applications of the multiquadric-biharmonic method (Pergamon Press plc, 1990), 163–208. [16] R. Schaback, Approximations: from CAGD to wavelets, chap-ter Comparison of radial basis function interpolants (WorldScientific, 1993), 293–305. [17] M.J.D. Powell, Approximation theory and methods (Cambridge,UK: Cambridge University Press, 1981). [18] M.J.D. Powell, Radial basis function for interpolation to func-tion of many variables. Technical Report DAMTP NA11, De-partment of Applied Mathematics and Theoretical Physics(Cambridge, UK: Cambridge University, 2001). [19] H.-M. Gutmann, A radial basis function method for globaloptimization. Technical Report DAMTP NA22, Departmentof Applied Mathematics and Theoretical Physics (Cambridge,UK: Cambridge University, 1999). [20] J.-E. K¨ack, Constrained global optimization with radial basisfunctions. Technical Report, Department of Mathematics andPhysics, M¨alardalen University, 2004. [21] R. Schaback & H. Wendland, Characterization and constructionof radial basis functions, in N. Dyn, D. Leviatan, D. Levin, &A. Pinkus (Eds.), Multivariate approximation and applications(Cambridge University Press, 2001), 1–24. [22] J.E. Dennis & R.B. Schnabel, Numerical methods for uncon-strained optimization and nonlinear equations. (Philadelphia,PA: Society for Industrial and Applied Mathematics (SIAM),1996). [23] 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. [24] E.D. Dolan & J.J. Mor´e, Benchmarking optimization soft-ware with performance profiles, Mathematical Programming,Series A, 91, 2002, 201–213. [25] R. Oeuvray & M. Bierlaire, A new derivative-free algorithm forthe medical image registration problem, International Journalof Modelling and Simulation, 27(2), 2007, 115–124.35
Important Links:
Go Back