Nonlinear Optimization Examples


References

  • Abramowitz, M., and Stegun, I. A., eds. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 10th printing. New York: Dover.

  • 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. Englewood Cliffs, NJ: 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.

  • Beale, E. M. L. (1972). “A Derivation of Conjugate Gradients.” In Numerical Methods for Nonlinear Optimization, edited by F. A. Lootsma, 39–43. 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 75:165–169.

  • 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 and Applications 28:453–482.

  • Dennis, J. E., and Schnabel, R. B. (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs, 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. 2nd ed. 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, P. E., Murray, W., Saunders, M. A., and Wright, M. H. (1983). “Computing Forward-Difference Intervals for Numerical Optimization.” SIAM Journal on Scientific and Statistical Computing 4:310–321.

  • Gill, P. E., 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, P. E., 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. M. (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. Vol. 187 of Lecture Notes in Economics and Mathematical Systems. Berlin: 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 & Sons.

  • Liebman, J., Lasdon, L., Schrage, L., and Waren, A. (1986). Modeling and Optimization with GINO. Redwood City, CA: 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 Lecture Notes in Mathematics, vol. 30, edited by G. A. Watson, 105–116. Berlin: 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.” Journal of the Royal Statistical Society, Series C 22:86–91.

  • Polak, E. (1971). Computational Methods in Optimization. New York: 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 Lecture Notes in Mathematics, vol. 630, edited by G. A. Watson, 144–175. Berlin: Springer-Verlag.

  • Powell, M. J. D. (1982a). “Extensions to Subroutine VF02AD.” In Systems Modeling and Optimization, Lecture Notes in Control and Information Sciences, vol. 38, edited by R. F. Drenick, and F. Kozin, 529–538. Berlin: Springer-Verlag.

  • Powell, M. J. D. (1982b). VMCWD: A Fortran Subroutine for Constrained Optimization. Technical Report DAMTP 1982/NA4, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

  • Powell, M. J. D. (1992). A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation. Technical Report DAMTP 1992/NA5, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

  • 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.” In Optimization Techniques: Proceedings of the Eighth IFIP Conference on Optimization Techniques. Berlin: Springer-Verlag.

  • Schittkowski, K. (1987). More Test Examples for Nonlinear Programming Codes. Vol. 282 of Lecture Notes in Economics and Mathematical Systems. Berlin: 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.” Journal of the Royal Statistical Society, Series C 37:87–94.

  • Wedin, P. A., and Lindström, P. (1987). Methods and Software for Nonlinear Least Squares Problems. Technical Report No. UMINF 133.87, Umeå University, Sweden.

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