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Connectedness of the Set of Efficient Solutions for Generalized Systems

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Abstract

We introduce the concept of positive proper efficient solutions to the generalized system in this paper. We show that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of efficient solutions to the generalized system. We discuss also the connectedness of the set of efficient solutions for the generalized system with monotone bifunctions in real locally convex Hausdorff topological vector spaces.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330047, China

    X. H. Gong

  2. Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan

    J. C. Yao

Authors
  1. X. H. Gong
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  2. J. C. Yao
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Corresponding author

Correspondence to J. C. Yao.

Additional information

Communicated by F. Giannessi

This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC.

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Gong, X.H., Yao, J.C. Connectedness of the Set of Efficient Solutions for Generalized Systems. J Optim Theory Appl 138, 189–196 (2008). https://doi.org/10.1007/s10957-008-9378-2

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  • DOI: https://doi.org/10.1007/s10957-008-9378-2

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