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Nonlinear Optimization Examples |

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,"
*Journal of Optimization Theory and Applications*,
48, 359-377.

Anderson, B.D.O. 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*,
New York: John Wiley & Sons, Inc.

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

Betts, J. T. (1977),
"An Accelerated Multiplier Method for Nonlinear
Programming," *Journal of Optimization Theory and
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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.

De Jong, P. (1988),
"The Likelihood for a State Space Model,"
*Biometrika*, 75, 165-169.

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.

Eskow, E. and Schnabel, R.B. (1991),
"Algorithm 695: Software for a New Modified Cholesky
Factorization," *ACM Trans. Math. Software*,
17, 306-312.

Fletcher, R. (1987),
*Practical Methods of Optimization*,
Second Ed., Chichester: John Wiley & Sons, Inc.

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 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.

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*,
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 Models and Methods for Lifetime Data*,
New York: John Wiley & Sons, Inc.

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

Lindstrm, P. and Wedin, P.A. (1984),
"A New Linesearch Algorithm for Nonlinear Least-Squares
Problems," *Mathematical Programming*, 29, 268-296.

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

Mor, J.J. (1978),
"The Levenberg-Marquardt Algorithm: Implementation and
Theory," *Lecture Notes in Mathematics 630*,
ed. G.A. Watson, New York: Springer-Verlag, 105-116.

Mor, J.J.; Garbow, B.S.; and Hillstrom, K.E. (1981),
"Testing Unconstrained Optimization Software,"
*ACM Trans. Math. Software*, 7, 17-41.

Mor, J.J. and Sorensen, D.C. (1983),
"Computing a Trust-Region Step,"
*SIAM J. Sci. Stat. Comput.*, 4, 553-572.

Mor, 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,"
*Appl. Statist*, 22, 86-91.

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

Powell, J.M.D. (1977),
"Restart Procedures for the Conjugate Gradient Method,"
*Mathematical Programming*, 12, 241-254.

Powell, J.M.D. (1978a),
"A Fast Algorithm for Nonlinearly Constrained Optimization
Calculations," *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, J.M.D. (1982a),
"Extensions to Subroutine VF02AD," *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," *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*, Heidelberg, New York:
Springer-Verlag.

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

Turnbull, B.W. (1976),
"The Empirical Distribution Function from Arbitrarily
Grouped, Censored and Truncated Data,"
*J. Royal Statist. Soc. Ser. 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 Lindstrm, P. (1987),
*Methods and Software for Nonlinear Least Squares Problems*,
University of Umea, Report No. UMINF 133.87.

Ziegel, E. R. and J. W. Gorman (1980),
"Kinetic Modelling with Multipurpose Data,"
*Technometrics*, 27, 352-357.

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