Chapter Contents
Chapter Contents
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 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.

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.

Lindstr\ddot{o}m, P. and Wedin, P.A. (1984), "A New Linesearch Algorithm for Nonlinear Least-Squares Problems," Mathematical Programming, 29, 268-296.

L\ddot{u}tkepohl, H. (1991), Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag.

Mor\acute{e}, 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\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," 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 Lindstr\ddot{o}m, 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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