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**Connectedness of efficient solution sets for set-valued maps in normed spaces.**
*(English)*
Zbl 0845.90104

A new interesting step is reported to find out conditions for vector optimization problems such that the connectedness of efficient sets follows. Here, the density theorem of Arrow-Barankin and Blackwell [look at Contribution to the Theory of Games, H. W. Kuhn, A. W. Tucker (eds.), Princeton University Press, 87-92 (1953; Zbl 0041.25302)] has been generalized so that it could be applied to vector optimization problems with point-to-set functions \(f: A\to Y\), where \(A\) is a set in a Hausdorff space \(X\) and \(Y\) is a real normed space.

Reviewer: A.Göpfert (Halle)

### MSC:

90C29 | Multi-objective and goal programming |

90C48 | Programming in abstract spaces |

54C60 | Set-valued maps in general topology |

### Keywords:

vector optimization; connectedness of efficient sets; theorem of Arrow-Barankin and Blackwell; point-to-set functions### Citations:

Zbl 0041.25302
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\textit{X. H. Gong}, J. Optim. Theory Appl. 83, No. 1, 83--96 (1994; Zbl 0845.90104)

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### References:

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