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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 108184, 13 pages
http://dx.doi.org/10.1155/2014/108184
Research Article

Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications

Department of Chemistry and Center for Theoretical and Computational Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 14 March 2014; Accepted 24 May 2014; Published 27 August 2014

Academic Editor: Mariano Torrisi

Copyright © 2014 Christopher Gunaseelan Jesudason. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. D. Craven, Functions of Several Variables, Chapman & Hall, London, UK, 1981. View at MathSciNet
  2. J. DePree and C. Swartz, Introduction to Real Analysis, John Wiley & Sons, New York, NY, USA, 1988. View at MathSciNet
  3. T. M. Apostol, Mathematical Analysis, Narosa Publishing House, New Delhi, India, 2nd edition, 2002.
  4. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes—The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 3rd edition, 2007. View at MathSciNet
  5. J. A. Snyman, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms, Springer, New York, NY, USA, 2005. View at MathSciNet
  6. W. C. Davidon, “Variable metric method for minimization,” SIAM Journal on Optimization, vol. 1, no. 1, pp. 1–17, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. G. Broyden, “The convergence of a class of double-rank minimization algorithms,” Journal of the Institute of Mathematics and Its Applications, vol. 6, pp. 76–90, 1970. View at Google Scholar
  8. A. Banerjee, N. Adams, J. Simons, and R. Shepard, “Search for stationary points on surfaces,” Journal of Physical Chemistry, vol. 89, no. 1, pp. 52–57, 1985. View at Google Scholar · View at Scopus
  9. D. A. Wales, Energy Landscapes, Cambridge Molecular Science, Cambridge University Press, Cambridge, UK, 2003, edited by R. Saykally, A. Zewail and D. King.
  10. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” The American Association for the Advancement of Science. Science, vol. 220, no. 4598, pp. 671–680, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Applications, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, NY, USA, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  12. G. H. Golub and V. Pereyra, “The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,” SIAM Journal on Numerical Analysis, vol. 10, pp. 413–432, 1973. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. H. M. van Stokkum, D. S. Larsen, and R. van Grondelle, “Global and target analysis of time-resolved spectra,” Biochimica et Biophysica Acta—Bioenergetics, vol. 1657, no. 2-3, pp. 82–104, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. P. Shearer and A. C. Gilbert, “A generalization of variable elimination for separable inverse problems beyond least squares,” Inverse Problems, vol. 29, no. 4, Article ID 045003, 27 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. N. I. M. Gould, Y. Loh, and D. P. Robinson, “A filter method with unified step computation for nonlinear optimization,” SIAM Journal on Optimization, vol. 24, no. 1, pp. 175–209, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  16. A. Milzarek and M. Ulbrich, “A semismooth Newton method with multidimensional filter globalization for l1-optimization,” SIAM Journal on Optimization, vol. 24, no. 1, pp. 298–333, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. M. Gomes, “Truss optimization with dynamic constraints using a particle swarm algorithm,” Expert Systems with Applications, vol. 38, no. 1, pp. 957–968, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Gendreau and J.-Y. Potvin, Eds., Handbook of Metaheuristics, vol. 146 of International Series in Operations Research & Management Science, Springer, New York, NY, USA, 2nd edition, 2010.
  19. R. Varadhan and P. D. Gilbert, “BB: an R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function,” Journal of Statistical Software, vol. 32, no. 4, pp. 1–26, 2009. View at Google Scholar · View at Scopus
  20. F. M. P. Raupp, L. M. G. Drummond, and B. F. Svaiter, “A quadratically convergent Newton method for vector optimization,” Optimization, vol. 63, no. 5, pp. 661–677, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. D. Al-Khaleel, M. J. Gander, and A. E. Ruehli, “Optimization of transmission conditions in waveform relaxation techniques for RC circuits,” SIAM Journal on Numerical Analysis, vol. 52, no. 2, pp. 1076–1101, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. Amirteimoori, D. K. Despotis, and S. Kordrostami, “Variables reduction in data envelopment analysis,” Optimization, vol. 63, no. 5, pp. 735–745, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  23. S. Solar, W. Solar, and N. Getoff, “A pulse radiolysis-computer simulation method for resolving of complex kinetics and spectra,” Radiation Physics and Chemistry, vol. 21, no. 1-2, pp. 129–138, 1983. View at Google Scholar · View at Scopus
  24. A.-M. Wazwaz, “A note on using Adomian decomposition method for solving boundary value problems,” Foundations of Physics Letters, vol. 13, no. 5, pp. 493–498, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  25. J. J. Houser, “Estimation of A in reaction-rate studies,” Journal of Chemical Education, vol. 59, no. 9, pp. 776–777, 1982. View at Google Scholar · View at Scopus
  26. P. Moore, “Analysis of kinetic data for a first-order reaction with unknown initial and final readings by the method of non-linear least squares,” Journal of the Chemical Society, Faraday Transactions I: Physical Chemistry in Condensed Phases, vol. 68, pp. 1890–1893, 1972. View at Publisher · View at Google Scholar · View at Scopus
  27. W. E. Wentworth, “Rigorous least squares adjustment: application to some non-linear equations, I,” Journal of Chemical Education, vol. 42, no. 2, pp. 96–103, 1965. View at Google Scholar · View at Scopus
  28. W. E. Wentworth, “Rigorous least squares adjustment: application to some non-linear equations, II,” Journal of Chemical Education, vol. 42, no. 3, pp. 162–167, 1965. View at Google Scholar · View at Scopus
  29. C. G. Jesudason, “The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics,” Journal of Mathematical Chemistry, vol. 43, no. 3, pp. 976–1023, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. M. N. Khan, Micellar Catalysis, vol. 133 of Surfactant Science Series, Taylor & Francis, Boca Raton, Fla, USA, 2007, edited by A. T. Hubbard.
  31. T. W. Newton and F. B. Baker, “The kinetics of the reaction between plutonium(VI) and iron(II),” Journal of Physical Chemistry, vol. 67, no. 7, pp. 1425–1432, 1963. View at Google Scholar · View at Scopus
  32. J. H. Espenson, Chemical Kinetics and Reaction Mechanisms, vol. 102, McGraw-Hill, Singapore, 2nd edition, 1995.