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Numerical Procedures in Multiobjective Optimization with Variable Ordering Structures

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  • Gabriele Eichfelder

    (Ilmenau University of Technology)

Abstract

Multiobjective optimization problems with a variable ordering structure, instead of a partial ordering, have recently gained interest due to several applications. In the previous years, a basic theory has been developed for such problems. The binary relations of a variable ordering structure are defined by a cone-valued map that associates, with each element of the linear space ℝ m , a pointed convex cone of dominated or preferred directions. The difficulty in the study of the variable ordering structures arises from the fact that the binary relations are in general not transitive. In this paper, we propose numerical approaches for solving such optimization problems. For continuous problems a method is presented using scalarization functionals, which allows the determination of an approximation of the infinite optimal solution set. For discrete problems the Jahn–Graef–Younes method, known from multiobjective optimization with a partial ordering, is adapted to allow the determination of all optimal elements with a reduced effort compared to a pairwise comparison.

Suggested Citation

  • Gabriele Eichfelder, 2014. "Numerical Procedures in Multiobjective Optimization with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 489-514, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0267-y
    DOI: 10.1007/s10957-013-0267-y
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    References listed on IDEAS

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    1. G. Y. Chen & X. Q. Yang, 2002. "Characterizations of Variable Domination Structures via Nonlinear Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 97-110, January.
    2. Gang Xiao & Hong Xiao & Sanyang Liu, 2011. "Scalarization and pointwise well-posedness in vector optimization problems," Journal of Global Optimization, Springer, vol. 49(4), pages 561-574, April.
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    Cited by:

    1. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 947-963, December.

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