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Global Optimization for the Sum of Certain Nonlinear Functions

Author

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  • Mio Horai
  • Hideo Kobayashi
  • Takashi G. Nitta

Abstract

We extend work by Pei‐Ping and Gui‐Xia, 2007, to a global optimization problem for more general functions. Pei‐Ping and Gui‐Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei‐Ping and Gui‐Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm.

Suggested Citation

  • Mio Horai & Hideo Kobayashi & Takashi G. Nitta, 2014. "Global Optimization for the Sum of Certain Nonlinear Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:408918
    DOI: 10.1155/2014/408918
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    References listed on IDEAS

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    1. Shen Pei-Ping & Yuan Gui-Xia, 2007. "Global optimization for the sum of generalized polynomial fractional functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 445-459, June.
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    Cited by:

    1. Mio Horai & Hideo Kobayashi & Takashi G. Nitta, 2016. "A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).

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