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Properly optimal elements in vector optimization with variable ordering structures

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Abstract

In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.

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Acknowledgments

The authors are grateful to Truong Xuan Duc Ha from the Institute of Mathematics in Hanoi for valuable comments on the elements of the augmented dual cone of a Bishop-Phelps cone. The research of this work was supported by the grant EI 821/2-1 from the Deutsche Forschungsgesellschaft (DFG) and was mainly prosecuted during a stay of the second author at the Institute of Mathematics, Technische Universität Ilmenau.

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Authors and Affiliations

  1. Institute of Mathematics, Technische Universität Ilmenau, PO 10 05 65, 98684 , Ilmenau, Germany

    Gabriele Eichfelder

  2. Department of Industrial Engineering, Faculty of Engineering, Anadolu University, Iki Eylul Campus, 26470 , Eskisehir, Turkey

    Refail Kasimbeyli

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  1. Gabriele Eichfelder
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  2. Refail Kasimbeyli
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Correspondence to Gabriele Eichfelder.

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Eichfelder, G., Kasimbeyli, R. Properly optimal elements in vector optimization with variable ordering structures. J Glob Optim 60, 689–712 (2014). https://doi.org/10.1007/s10898-013-0132-4

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