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A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

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  • Mio Horai
  • Hideo Kobayashi
  • Takashi G. Nitta

Abstract

We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:1304954
    DOI: 10.1155/2016/1304954
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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.
    2. 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).
    3. Mio Horai & Hideo Kobayashi & Takashi G. Nitta, 2014. "Global Optimization for the Sum of Certain Nonlinear Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, November.
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