The NLP Procedure

References

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

Al-Baali, M., and Fletcher, R. (1985), "Variational methods for nonlinear least squares", J. Oper. Res. Soc., 36, 405-421.

Al-Baali, M., and Fletcher, R. (1986), "An efficient line search for nonlinear least squares", J. Optimiz. Theory Appl., 48, 359-377.

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

Beale, E.M.L. (1972), "A derivation of conjugate gradients", In: F.A. Lootsma (ed.), Numerical Methods for Nonlinear Optimization, Academic Press, London.

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, Inc.

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 University Press, Cambridge, England.

Dennis, J.E., Gay, D.M., and Welsch, R.E. (1981), "An adaptive nonlinear least-squares algorithm", ACM Trans. Math. Software, 7, 348-368.

Dennis, J.E., and Mei, H.H.W. (1979), ``Two new unconstrained optimization algorithms which use function and gradient values'', J. Optim. Theory Appl., 28, 453-482.

Dennis, J.E. and Schnabel, R.B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, New Jersey: Prentice-Hall.

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

Fletcher, R., and Powell, M.J.D. (1963), "A rapidly convergent descent method for minimization", Comput.J., 6, 163-168.

Fletcher, R., and Xu, C. (1987), "Hybrid methods for nonlinear least squares", J. 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 Trans. Math. Software, 9, 503-524.

George, J.A. and Liu, J.W. (1981), Computer Solution of Large Sparse Positive Definite Systems, New Jersey: Prentice-Hall.

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

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 Trans. Math. Software, 10, 282-298.

Goldfeld, S.M., Quandt, R.E., & 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. (1992), Nonlinear Optimization in IML, Releases 6.08, 6.09, 6.10; Technical Report, Cary, N.C.: SAS Institute Inc.

Hartmann, W. (1992), Applications of Nonlinear Optimization with PROC NLP and SAS/IMLSoftware, Technical Report, Cary, N.C.: SAS Institute Inc.

Haverly, C.A. (1978), "Studies of the behavior of recursion for the pooling problem", SIGMAP Bulletin, Association for Computing Machinery.

Hock, W., and Schittkowski, K. (1981), s for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems 187, Springer Verlag, Berlin-Heidelberg-New York.

Jennrich, R.I., and Sampson, P.F. (1968), "Application of stepwise regression to nonlinear estimation", Technometrics, 10, 63-72.

Liebman, J.; Lasdon, L.; Schrage, L.; and Waren, A. (1986), Modeling and Optimization with GINO, California: The Scientific Press.

Lindstr $\ddot{o}$ m, P., and Wedin, P.A. (1984), "A new linesearch algorithm for nonlinear least-squares problems", Math. Prog., 29, 268-296.

Mor $\acute{e}$ , J.J. (1978), "The Levenberg-Marquardt Algorithm: Implementation and Theory", In: G.A. Watson (ed.), Lecture Notes in Mathematics 630, Springer Verlag, Berlin-Heidelberg-New York, 105-116.

Mor $\acute{e}$ , J.J., Garbow, B.S., and Hillstrom, K.E. (1981), "Testing unconstrained optimization software", ACM Trans. Math. Software, 7, 17-41.

Mor $\acute{e}$ , J.J., and Sorensen, D.C. (1983), "Computing a trust-region step", SIAM J. Sci. Stat. Comput., 4, 553-572.

Mor $\acute{e}$ , J.J. and Sorensen, D.C. (1983), "Computing a Trust-Region Step", SIAM J. Sci. Stat. Comput., 4, 553-572.

Mor $\acute{e}$ , 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", Comput. J., 7, 308-313.

Polak, E. (1971), Computational Methods in Optimization, Academic Press, New York - San Francisco - London.

Powell, J.M.D. (1977), "Restart procedures for the conjugate gradient method", Math. Prog., 12, 241-254.

Powell, J.M.D. (1978a), ``A fast algorithm for nonlinearly constraint optimization calculations'', in Numerical Analysis, Dundee 1977, Lecture Notes in Mathematics 630, ed. G.A. Watson, Springer Verlag, Berlin, 144-175.

Powell, J.M.D. (1978b), ``Algorithms for nonlinear constraints that use Lagrangian functions'', Mathematical Programming, 14, 224-248.

Powell, M.J.D. (1982a), "Extensions to subroutine VF02AD", in Systems Modeling and Optimization, Lecture Notes In Control and Information Sciences 38, eds. R.F. Drenick and F. Kozin, Springer Verlag, Berlin, 529-538.

Powell, J.M.D. (1982b), "VMCWD: A Fortran subroutine for constrained optimization", DAMTP 1982/NA4, Cambridge, England.

Powell, J.M.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'', Comput. J., 3, 175-184.

Schittkowski, K. (1980), Nonlinear Programming Codes - Information, Tests, Performance Lecture Notes in Economics and Mathematical Systems 183, Springer Verlag, Berlin-Heidelberg-New York.

Schittkowski, K. (1987), More s for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems 282, Springer Verlag, Berlin-Heidelberg-New York.

Schittkowski, K. and Stoer, J. (1979), ``A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing Subsequent Data Changes'', Numer. Math., 31, 431-463.

Stewart, G.W. (1967), ``A modification of Davidon's minimization method to accept difference approximations of derivatives'', J. Assoc. Comput. Mach. 14 72-83.

Wedin, P.A., and Lindstr $\ddot{o}$ m, P. (1987), Methods and software for nonlinear least squares problems, University of Umea, Report No. UMINF 133.87.

Whitaker,D., Triggs, C.M., and John, J.A. (1990), "Construction of Block Designs using Mathematical Programming", J. R. Statist. Soc. B, 52, 497-503.

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