Globally proper saddle point in ic-cone-convexlike set-valued optimization problems

Yu, G.; Liu, San Yang

doi:10.1007/s10114-009-6144-9

Cited by 10 publications

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“…This kind of proper efficiency has been drawn much attention in recent years, see Refs. [5,310 GUOLIN YU 8-9, [22][23]. It is worthy to notice that Henig globally efficiency and Benson proper efficiency [2] are equivalent when the partial ordering convex cone is pointed and closed (see Refs [9]).…”

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confidence: 99%

“…The following Lemma 2.2 is cited from Ref. [23], which shows that the existence of Henig globally efficient points for a nonempty subset just need weakly sequentially compactness, and it will be used in the sequel. Now, we recall the notion of ic-cone-convexlikeness for a nonempty set, which was introduced by Sach [17], and present an example for this kind of generalized cone-convexity.…”

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confidence: 99%

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Topological properties of Henig globally efficient solutions of set-valued problems

Yu¹

2014

Numerical Algebra, Control &Amp; Optimization

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This paper deals with the topological properties of Henig globally efficiency in vector optimization problem with set-valued mapping. The closednesst and compactness results are presented for Henig globally efficiency, Especially, under the assumption of ic-cone-convexlikeness, the connectedness of Henig globally efficient set is obtained. As the application of the results, the relevant topological properties of Benson proper efficiency are also presented.

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confidence: 99%

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confidence: 99%