We introduce the notion of sectionwise connected set as a new tool to investigate nonconvex vector optimization. Indeed, the image of a K-convex set through a K-quasiconnected vector function is proved to be sectionwise connected. Some properties of the minimal frontiers of sectionwise connected sets are studied.
Miglierina, E., Molho, E., Sectionwise connected sets in vector optimization, <<OPERATIONS RESEARCH LETTERS>>, 2009; 37 (4): 295-298. [doi:10.1016/j.orl.2009.03.012] [http://dx.medra.org/10.1016/j.orl.2009.03.012] [http://hdl.handle.net/10807/1379]
Sectionwise connected sets in vector optimization
Miglierina, Enrico;
2009
Abstract
We introduce the notion of sectionwise connected set as a new tool to investigate nonconvex vector optimization. Indeed, the image of a K-convex set through a K-quasiconnected vector function is proved to be sectionwise connected. Some properties of the minimal frontiers of sectionwise connected sets are studied.
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