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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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