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Convexification of a Noninferior Frontier

Author

Listed:
  • C. J. Goh

    (University of Western Australia)

  • X. Q. Yang

    (University of Western Australia)

Abstract

In a recent paper by Li (Ref. 1), a scheme was proposed to convexify an efficient frontier for a vector optimization problem by rescaling each component of the vector objective functions by its p-power. For sufficiently large p, it was shown that the transformed efficient frontier is cone-convex; hence, the usual linear scalarization (or supporting hyperplane) method can be used to find the efficient solutions. An outstanding question remains: What is the minimum value of p such that the efficient frontier can be convexified? In this note, we answer the above question by deriving some theoretical lower bounds for p.

Suggested Citation

  • C. J. Goh & X. Q. Yang, 1998. "Convexification of a Noninferior Frontier," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 759-768, June.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:3:d:10.1023_a:1022654528902
    DOI: 10.1023/A:1022654528902
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    Cited by:

    1. Masoud Zarepisheh & Panos M. Pardalos, 2017. "An equivalent transformation of multi-objective optimization problems," Annals of Operations Research, Springer, vol. 249(1), pages 5-15, February.

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