The NLP Procedure

References

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

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, 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 and 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, England: Cambridge University Press.

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 that 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. second edition, Chichester: John Wiley and 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 and 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.; 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. (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/IML Software, 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, Berlin-Heidelberg-New York: 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 and Sons, Inc.

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 Line-Search 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, Berlin-Heidelberg-New York: Springer Verlag, 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 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, New York - San Francisco - London: Academic Press.

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, Berlin: Springer Verlag, 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, Berlin: Springer Verlag, 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, Berlin-Heidelberg-New York: Springer Verlag.

Schittkowski, K. (1987), More s for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems 282, 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'', 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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