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Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems

Author

Listed:
  • Washington Alves Oliveira

    (University of Campinas)

  • Marko Antonio Rojas-Medar

    (Universidad de Tarapacá)

  • Antonio Beato-Moreno

    (University of Sevilla)

  • Maria Beatriz Hernández-Jiménez

    (Universidad Pablo de Olavide)

Abstract

If $$x^*$$ x ∗ is a local minimum solution, then there exists a ball of radius $$r>0$$ r > 0 such that $$f(x)\ge f(x^*)$$ f ( x ) ≥ f ( x ∗ ) for all $$x\in B(x^*,r)$$ x ∈ B ( x ∗ , r ) . The purpose of the current study is to identify the suitable $$B(x^*,r)$$ B ( x ∗ , r ) of the local optimal solution $$x^*$$ x ∗ for a particular multiobjective optimization problem. We provide a way to calculate the largest radius of the ball centered at local Pareto solution in which this solution is optimal. In this process, we present the necessary and sufficient conditions for achieving a global Pareto optimal solution. The results of this investigation might be useful to determine stopping criteria in the algorithms development.

Suggested Citation

  • Washington Alves Oliveira & Marko Antonio Rojas-Medar & Antonio Beato-Moreno & Maria Beatriz Hernández-Jiménez, 2019. "Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems," Journal of Global Optimization, Springer, vol. 74(2), pages 233-253, June.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:2:d:10.1007_s10898-019-00766-1
    DOI: 10.1007/s10898-019-00766-1
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    References listed on IDEAS

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