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Connectedness of super efficient solution sets for set-valued maps in Banach spaces

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Abstract

In this paper, we study the connectedness of the super efficient solution sets in convex vector optimization for set-valued maps in Banach spaces.

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References

  1. Aubin JP, Ekeland I (1984) Applied nonlinear analysis. John Wiley and Sons, New York, New York

    Google Scholar 

  2. Borwein JM, Zhuang DM (1993) Super efficiency in vector optimization. Trans Amer Math Soc 338:105–122

    Google Scholar 

  3. Borwein JM, Zhuang DM (1991) Super efficiency in convex vector optimization. ZOR 35:175–184

    Google Scholar 

  4. Fu WT, Zhou KP (1993) Connectedness of the efficient solution sets for a strictly path quasi-convex programming problem. Nonlinear Analysis 21 (12) 903–910

    Google Scholar 

  5. Gong XH (1993) Connectedness of efficient solution sets for cone-strongly quasiconvex set-valued maps in topological vector lattice. J Nanchang Univ 17(3): 94–98

    Google Scholar 

  6. Gong XH (1994) Connectedness of efficient solution sets for set-valued maps in normed spaces. JOTA 83(1): 83–96

    Google Scholar 

  7. Hu YD, Hu YF (1989) Cone quasiconvexity and the connectedness of sets of efficient and weak efficient solution to multiobjective optimization. Acta Math Appl Sin 21:115–123

    Google Scholar 

  8. Helbig S (1990) On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces. JOTA 65(2): 257–270

    Google Scholar 

  9. Jahn J (1986) Mathematical vector optimization in partially ordered linear spaces. Verlag Peter Lang, Frankfurt/Main

    Google Scholar 

  10. Luc DT (1990) Contractibility of efficient point sets in normed spaces. Nonlinear Analysis 15:527–535

    Google Scholar 

  11. Warburton AR (1983) Quasiconcave vector maximization: connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives. JOTA 40:537–557

    Google Scholar 

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Authors and Affiliations

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

    X. H. Gong

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  1. X. H. Gong
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Gong, X.H. Connectedness of super efficient solution sets for set-valued maps in Banach spaces. Mathematical Methods of Operations Research 44, 135–145 (1996). https://doi.org/10.1007/BF01246333

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  • DOI: https://doi.org/10.1007/BF01246333

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