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Scalarization of \(\epsilon \)-Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces

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Abstract

In this paper, we investigate the scalarization of \(\epsilon \)-super efficient solutions of set-valued optimization problems in real ordered linear spaces. First, in real ordered linear spaces, under the assumption of generalized cone subconvexlikeness of set-valued maps, a dual decomposition theorem is established in the sense of \(\epsilon \)-super efficiency. Second, as an application of the dual decomposition theorem, a linear scalarization theorem is given. Finally, without any convexity assumption, a nonlinear scalarization theorem characterized by the seminorm is obtained.

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Acknowledgments

This work was supported by the National Nature Science Foundation of China (11271391) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ130830).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, China

    Zhi-Ang Zhou

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

    Xin-Min Yang

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  1. Zhi-Ang Zhou
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  2. Xin-Min Yang
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Correspondence to Xin-Min Yang.

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Zhou, ZA., Yang, XM. Scalarization of \(\epsilon \)-Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces. J Optim Theory Appl 162, 680–693 (2014). https://doi.org/10.1007/s10957-014-0565-z

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  • DOI: https://doi.org/10.1007/s10957-014-0565-z

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