On connectedness of efficient solution sets for a star cone-quasiconvex vector optimization problem

Wen Song; Bo Ying Wu; Jian Mei Zhang

doi:10.1007/s10255-006-0352-1

On connectedness of efficient solution sets for a star cone-quasiconvex vector optimization problem

Wen Song^*
, Bo Ying Wu
, Jian Mei Zhang

^*Corresponding author for this work

School of Mathematics

Harbin Normal University
Guangdong University of Foreign Studies

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.

Original language	English
Pages (from-to)	91-98
Number of pages	8
Journal	Acta Mathematicae Applicatae Sinica
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s10255-006-0352-1
State	Published - Jan 2007

Keywords

Connectivity
D-cone
Efficient point set
Vector optimization

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10.1007/s10255-006-0352-1

Cite this

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title = "On connectedness of efficient solution sets for a star cone-quasiconvex vector optimization problem",

abstract = "In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.",

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AU - Wu, Bo Ying

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AB - In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.

KW - Connectivity

KW - D-cone

KW - Efficient point set

KW - Vector optimization

UR - https://www.scopus.com/pages/publications/33845762720

U2 - 10.1007/s10255-006-0352-1

DO - 10.1007/s10255-006-0352-1

M3 - 文章

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IS - 1

ER -

On connectedness of efficient solution sets for a star cone-quasiconvex vector optimization problem

Abstract

Keywords

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