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The semi-E cone convex set-valued map and its applications

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Abstract

In this paper, firstly, a new notion of the semi-E cone convex set-valued map is introduced in locally convex spaces. Secondly, without any convexity assumption, we investigate the existence conditions of the weakly efficient element of the set-valued optimization problem. Finally, under the assumption of the semi-E cone convexity of set-valued maps, we obtain that the local weakly efficient element of the set-valued optimization problem is the weakly efficient element. We also give some examples to illustrate our results.

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Acknowledgements

This work was supported by the National Nature Science Foundation of China (11431004,11471291), the General Project of Chongqing Frontier and Applied Foundation Research (cstc2015jcyjA00050), the Key Project of Chongqing Frontier and Applied Foundation Research (cstc2017jcyjBX0055, cstc2015jcyjBX0113) and the Science and Technology Project of Chongqing Municipal Education Commission (KJ1605201).

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Authors and Affiliations

  1. College of Sciences, Chongqing University of Technology, Chongqing, 400054, China

    Zhi-Ang Zhou

  2. College of Mathematical Sciences, Chongqing Normal University, Chongqing, 400047, China

    Xin-Min Yang

  3. Department of Foundation, Chongqing Telecommunication Polytechnic College, Chongqing, 402247, China

    Xuan Wan

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

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Zhou, ZA., Yang, XM. & Wan, X. The semi-E cone convex set-valued map and its applications. Optim Lett 12, 1329–1337 (2018). https://doi.org/10.1007/s11590-017-1169-y

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  • DOI: https://doi.org/10.1007/s11590-017-1169-y

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