References

  • Abramowitz, M. and Stegun, I. A. (1972), Handbook of Mathematical Functions, New York: Dover Publications.

  • Al-Baali, M. and Fletcher, R. (1985), “Variational Methods for Nonlinear Least Squares,” Journal of the Operations Research Society, 36, 405–421.

  • Al-Baali, M. and Fletcher, R. (1986), “An Efficient Line Search for Nonlinear Least Squares,” Journal of Optimization Theory and Applications, 48, 359–377.

  • Bard, Y. (1974), Nonlinear Parameter Estimation, New York: Academic Press.

  • Beale, E. M. L. (1972), “A Derivation of Conjugate Gradients,” in F. A. Lootsma, ed., Numerical Methods for Nonlinear Optimization, London: Academic Press.

  • Betts, J. T. (1977), “An Accelerated Multiplier Method for Nonlinear Programming,” Journal of Optimization Theory and Applications, 21, 137–174.

  • Bracken, J. and McCormick, G. P. (1968), Selected Applications of Nonlinear Programming, New York: John Wiley & Sons.

  • Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., and Pedersen, H. C. (1982), “The Watchdog Technique for Forcing Convergence in Algorithms for Constrained Optimization,” Mathematical Programming, 16, 1–17.

  • Cramer, J. S. (1986), Econometric Applications of Maximum Likelihood Methods, Cambridge: Cambridge University Press.

  • Dennis, J. E., Gay, D. M., and Welsch, R. E. (1981), “An Adaptive Nonlinear Least-Squares Algorithm,” ACM Transactions on Mathematical Software, 7, 348–368.

  • Dennis, J. E. and Mei, H. H. W. (1979), “Two New Unconstrained Optimization Algorithms Which Use Function and Gradient Values,” Journal of Optimization Theory and Applications, 28, 453–482.

  • Dennis, J. E. and Schnabel, R. B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Englewood Cliffs, NJ: Prentice-Hall.

  • Eskow, E. and Schnabel, R. B. (1991), “Algorithm 695: Software for a New Modified Cholesky Factorization,” ACM Transactions on Mathematical Software, 17, 306–312.

  • Fletcher, R. (1987), Practical Methods of Optimization, 2nd Edition, Chichester, UK: John Wiley & Sons.

  • Fletcher, R. and Powell, M. J. D. (1963), “A Rapidly Convergent Descent Method for Minimization,” Computer Journal, 6, 163–168.

  • Fletcher, R. and Xu, C. (1987), “Hybrid Methods for Nonlinear Least Squares,” Journal of Numerical Analysis, 7, 371–389.

  • Gallant, A. R. (1987), Nonlinear Statistical Models, New York: John Wiley & Sons.

  • Gay, D. M. (1983), “Subroutines for Unconstrained Minimization,” ACM Transactions on Mathematical Software, 9, 503–524.

  • George, J. A. and Liu, J. W. (1981), Computer Solutions of Large Sparse Positive Definite Systems, Englewood Cliffs, NJ: Prentice-Hall.

  • Gill, E. P., Murray, W., Saunders, M. A., and Wright, M. H. (1983), “Computing Forward-Difference Intervals for Numerical Optimization,” SIAM Journal on Scientific and Statistical Computing, 4, 310–321.

  • Gill, E. P., Murray, W., Saunders, M. A., and Wright, M. H. (1984), “Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints,” ACM Transactions on Mathematical Software, 10, 282–298.

  • Gill, P. E., Murray, W., and Wright, M. H. (1981), Practical Optimization, New York: Academic Press.

  • Goldfeld, S. M., Quandt, R. E., and Trotter, H. F. (1966), “Maximisation by Quadratic Hill-Climbing,” Econometrica, 34, 541–551.

  • Hambleton, R. K., Swaminathan, H., and Rogers, H. J. (1991), Fundamentals of Item Response Theory, Newbury Park, CA: Sage Publications.

  • Hartmann, W. M. (1992a), Applications of Nonlinear Optimization with PROC NLP and SAS/IML Software, Technical report, SAS Institute Inc., Cary, NC.

  • Hartmann, W. M. (1992b), Nonlinear Optimization in IML, Releases 6.08, 6.09, 6.10, Technical report, SAS Institute Inc., Cary, NC.

  • Haverly, C. A. (1978), “Studies of the Behavior of Recursion for the Pooling Problem,” SIGMAP Bulletin, Association for Computing Machinery, 25, 19–28.

  • Hock, W. and Schittkowski, K. (1981), Test Examples for Nonlinear Programming Codes, volume 187 of Lecture Notes in Economics and Mathematical Systems, Berlin: Springer-Verlag.

  • Jennrich, R. I. and Sampson, P. F. (1968), “Application of Stepwise Regression to Nonlinear Estimation,” Technometrics, 10, 63–72.

  • Lawless, J. F. (1982), Statistical Methods and Methods for Lifetime Data, New York: John Wiley & Sons.

  • Liebman, J., Lasdon, L., Schrage, L., and Waren, A. (1986), Modeling and Optimization with GINO, Redwood City, CA: Scientific Press.

  • Lindström, P. and Wedin, P. A. (1984), “A New Line-Search Algorithm for Nonlinear Least-Squares Problems,” Mathematical Programming, 29, 268–296.

  • Moré, J. J. (1978), “The Levenberg-Marquardt Algorithm: Implementation and Theory,” in G. A. Watson, ed., Lecture Notes in Mathematics, volume 30, 105–116, Berlin: Springer-Verlag.

  • Moré, J. J., Garbow, B. S., and Hillstrom, K. E. (1981), “Testing Unconstrained Optimization Software,” ACM Transactions on Mathematical Software, 7, 17–41.

  • Moré, J. J. and Sorensen, D. C. (1983), “Computing a Trust-Region Step,” SIAM Journal on Scientific and Statistical Computing, 4, 553–572.

  • Moré, J. J. and Wright, S. J. (1993), Optimization Software Guide, Philadelphia: SIAM.

  • Murtagh, B. A. and Saunders, M. A. (1983), MINOS 5.0 User’s Guide, Technical Report SOL 83-20, Stanford University.

  • Nelder, J. A. and Mead, R. (1965), “A Simplex Method for Function Minimization,” Computer Journal, 7, 308–313.

  • Polak, E. (1971), Computational Methods in Optimization, New York: Academic Press.

  • Powell, M. J. D. (1977), “Restart Procedures for the Conjugate Gradient Method,” Mathematical Programming, 12, 241–254.

  • Powell, M. J. D. (1978a), “Algorithms for Nonlinear Constraints That Use Lagrangian Functions,” Mathematical Programming, 14, 224–248.

  • Powell, M. J. D. (1978b), “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” in G. A. Watson, ed., Lecture Notes in Mathematics, volume 630, 144–175, Berlin: Springer-Verlag.

  • Powell, M. J. D. (1982a), “Extensions to Subroutine VF02AD,” in R. F. Drenick and F. Kozin, eds., Systems Modeling and Optimization, Lecture Notes in Control and Information Sciences, volume 38, 529–538, Berlin: Springer-Verlag.

  • Powell, M. J. D. (1982b), VMCWD: A Fortran Subroutine for Constrained Optimization, Technical Report DAMTP 1982/NA4, Cambridge University.

  • Powell, M. J. D. (1992), “A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation,” DAMTP/NA5.

  • Rosenbrock, H. H. (1960), “An Automatic Method for Finding the Greatest or Least Value of a Function,” Computer Journal, 3, 175–184.

  • Schittkowski, K. (1980), Nonlinear Programming Codes—Information, Tests, Performance, volume 183 of Lecture Notes in Economics and Mathematical Systems, Berlin: Springer-Verlag.

  • Schittkowski, K. (1987), More Test Examples for Nonlinear Programming Codes, volume 282 of Lecture Notes in Economics and Mathematical Systems, Berlin: Springer-Verlag.

  • Schittkowski, K. and Stoer, J. (1979), “A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing Subsequent Data Changes,” Numerische Mathematik, 31, 431–463.

  • Stewart, G. W. (1967), “A Modification of Davidon’s Minimization Method to Accept Difference Approximations of Derivatives,” Journal of the Association for Computing Machinery, 14, 72–83.

  • Wedin, P. A. and Lindström, P. (1987), Methods and Software for Nonlinear Least Squares Problems, Technical Report Report No. UMINF 133.87, University of Umea.

  • Whitaker, D., Triggs, C. M., and John, J. A. (1990), “Construction of Block Designs Using Mathematical Programming,” Journal of the Royal Statistical Society, Series B, 52, 497–503.

  • Wolfe, P. (1982), “Checking the Calculation of Gradients,” ACM Transactions on Mathematical Software, 8, 337–343.