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.

Anderson, B. D. and Moore, J. B. (1979), Optimal Filtering, New Jersey: Prentice-Hall.

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

Bates, D. M. and Watts, D. G. (1988), Nonlinear Regression Analysis and Its Applications, John Wiley & Sons.

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.

De Jong, P. (1988), “The Likelihood for a State Space Model,” Biometrika.

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 Applications, 28, 453–482.

Dennis, J. E. and Schnabel, R. B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Englewood, 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, Second 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.

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 J. Sci. Stat. Comput., 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, E. P., 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.

Hartmann, W. (1991), The NLP Procedure: Extended User’s Guide, Releases 6.08 and 6.10, Cary, NC: SAS Institute Inc.

Hock, W. and Schittkowski, K. (1981), “Test Examples for Nonlinear Programming Codes,” Lecture Notes in Economics and Mathematical Systems 187.

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, California: The Scientific Press.

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

Lütkepohl, H. (1991), Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag.

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-Heidelberg-New York: 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.

Peto, R. (1973), “Experimental Survival Curves for Interval-Censored Data,” Applied Statistics, 22, 86–91.

Polak, E. (1971), Computational Methods in Optimization, New York - San Francisco - London: 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-Heidelberg-New York: 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-Heidelberg-New York: Springer-Verlag.

Powell, M. J. D. (1982b), “VMCWD: A Fortran Subroutine for Constrained Optimization,” DAMTP 1982/NA4, cambridge, England.

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

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

Schittkowski, K. (1978), “An Adaptive Precision Method for the Numerical Solution of Constrained Optimization Problems Applied to a Time-Optimal Heating Process,” Proceedings of the 8th IFIP Conference on Optimization Techniques.

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

Turnbull, B. W. (1976), “The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data,” Journal of the Royal Statistical Society, Series B, 38, 290–295.

Venzon, D. J. and Moolgavkar, S. H. (1988), “A Method for Computing Profile-Likelihood Based Confidence Intervals,” Applied Statistics, 37, 87–94.

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

Ziegel, E. R. and Gorman, J. W. (1980), “Kinetic Modelling with Multipurpose Data,” Technometrics, 27, 352–357.