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Sensitivity Analysis of Merit Function in Solving Nonlinear Equations by Optimization

Author

Listed:
  • Seyyed Shahabeddin Azimi

    (Amirkabir University of Technology)

  • Mansour Kalbasi

    (Amirkabir University of Technology)

  • Hamidreza Sadeghifar

    (Simon Fraser University)

Abstract

To solve nonlinear equations by an optimization method, scaling is very important. Two types of poor scaling where: (a) the variables differ greatly in magnitude; (b) the merit function of system is highly sensitive to small changes in certain variables and relatively insensitive to changes in other variables. If poor scaling is ignored, the algorithm may produce solutions with poor quality. To solve (a), we can change units of variables. A numerical solution of the nonlinear equations produced by the finite volume method in the forced convective heat transfer of a nanofluid, as a case study, indicates that the poor scaling (b) is solved by using the Euclidean norm of columns of the Jacobian matrix as scaling data, while some researchers proposed diagonal elements of the Hessian matrix as scaling data.

Suggested Citation

  • Seyyed Shahabeddin Azimi & Mansour Kalbasi & Hamidreza Sadeghifar, 2014. "Sensitivity Analysis of Merit Function in Solving Nonlinear Equations by Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 191-201, July.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0439-9
    DOI: 10.1007/s10957-013-0439-9
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