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Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces

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  • Z. A. Zhou

    (Chongqing University of Technology)

  • J. W. Peng

    (Chongqing Normal University)

Abstract

In real ordered linear spaces, an equivalent characterization of generalized cone subconvexlikeness of set-valued maps is firstly established. Secondly, under the assumption of generalized cone subconvexlikeness of set-valued maps, a scalarization theorem of set-valued optimization problems in the sense of ϵ-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem of ϵ-global properly efficient element of set-valued optimization problems is obtained. The results in this paper generalize and improve some known results in the literature.

Suggested Citation

  • Z. A. Zhou & J. W. Peng, 2012. "Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 830-841, September.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0045-2
    DOI: 10.1007/s10957-012-0045-2
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    References listed on IDEAS

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    8. M. Adán & V. Novo, 2004. "Proper Efficiency in Vector Optimization on Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 515-540, June.
    9. Z. F. Li, 1998. "Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 623-649, September.
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    Cited by:

    1. Jian-Wen Peng & Wen-Bin Wei & Refail Kasimbeyli, 2025. "Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-21, July.
    2. Zhi-Ang Zhou & Xin-Min Yang, 2014. "Scalarization of $$\epsilon $$ ϵ -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 680-693, August.
    3. Elisabeth Köbis & Markus A. Köbis & Xiaolong Qin, 2020. "An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    4. C. Gutiérrez & L. Huerga & B. Jiménez & V. Novo, 2018. "Approximate solutions of vector optimization problems via improvement sets in real linear spaces," Journal of Global Optimization, Springer, vol. 70(4), pages 875-901, April.

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