Nonlinear Equation Solving

  • Hime Aguiar e Oliveira Junior
  • Lester Ingber
  • Antonio Petraglia
  • Mariane Rembold Petraglia
  • Maria Augusta Soares Machado
Part of the Intelligent Systems Reference Library book series (ISRL, volume 35)


This chapter introduces a global optimization approach for finding solutions of nonlinear systems of functional equations using Fuzzy ASA. The original problem is transformed into a global optimization one by synthesizing objective functions whose global minima, if any, are also solutions to the original system. The global minimization process is triggered from different starting points so as to find as many solutions as possible. To demonstrate its utility, the method is applied to several types of equations, presenting very good results. The equation systems are composed of n equations on n-dimensional Euclidean spaces.


Global Optimization Merit Function Polynomial System Search Region Solution Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  • Hime Aguiar e Oliveira Junior
    • 1
  • Lester Ingber
    • 2
  • Antonio Petraglia
    • 3
  • Mariane Rembold Petraglia
    • 3
  • Maria Augusta Soares Machado
    • 4
  1. 1.Rio de JaneiroBrazil
  2. 2.Lester Ingber Research AshlandUSA
  3. 3.Faculdades IBMEC Rio de JaneiroBrazil
  4. 4.IBMEC-RJ Rio de JaneiroBrazil

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