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\(\epsilon \)-Henig proper efficiency of set-valued optimization problems in real ordered linear spaces

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Abstract

The aim of this paper is to investigate \(\epsilon \)-Henig proper efficiency of set-valued optimization problems in linear spaces. Firstly, a new notion of \(\epsilon \)-Henig properly efficient point is introduced in linear spaces. Secondly, scalarization theorems of set-valued optimization problems are established in the sense of \(\epsilon \)-Henig proper efficiency. Finally, under the assumption of generalized cone subconvexlikeness, Lagrange multiplier theorems are obtained. Our results generalize some known results in the literature from topological spaces to linear spaces.

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Acknowledgments

Zhi-Ang Zhou was supported by the Natural Science Foundation of Chongqing (CSTC 2011jjA00022) and the Science and Technology Project of Chongqing Municipal Education Commission (KJ130830). Xin-Min Yang was supported by the National Nature Science Foundation of China (11271391) and the Natural Science Foundation of Chongqing (CSTC 2011BA0030). Jian-Wen Peng was supported by the National Nature Science Foundation of China (11171363), the project of the third batch support program for excellent talents of Chongqing City High Colleges and the Special Fund of Chongqing Key Laboratory (CSTC 2011KLORSE01).

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Authors and Affiliations

  1. Department of Applied Mathematics, Chongqing University of Technology, Chongqing, 400054, China

    Zhi-Ang Zhou

  2. School of Mathematics, Chongqing Normal University, Chongqing, 400047, China

    Xin-Min Yang & Jian-Wen Peng

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  1. Zhi-Ang Zhou
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  2. Xin-Min Yang
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  3. Jian-Wen Peng
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Correspondence to Jian-Wen Peng.

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Zhou, ZA., Yang, XM. & Peng, JW. \(\epsilon \)-Henig proper efficiency of set-valued optimization problems in real ordered linear spaces. Optim Lett 8, 1813–1827 (2014). https://doi.org/10.1007/s11590-013-0667-9

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  • DOI: https://doi.org/10.1007/s11590-013-0667-9

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