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Operations Research Transactions >

2016 , Vol. 20 >Issue 4: 21 - 29

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.04.003

A kind of cone-convexity for set-valued maps and its scalarization

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  • 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; 2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China; 3. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China

Received date: 2015-11-12

  Online published: 2016-12-15

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Abstract

In this paper, we firstly introduce the notion of scalar cone-quasiconvexity for set-valued maps and discuss the relationships among several cone-convexities. A characterization for proper cone-quasiconvexity of set-valued maps is also given in the sense of a type of level set. Meanwhile, the composition rule of cone-convexity of set-valued maps is established by scalar increasing convex functions. We obtain a characterization for cone-quasiconvexity of set-valued maps by Gerstewitz functional finally.

Key words： set-valued maps; cone-convexity; Gerstewitz functional; scalarizations

Cite this article

LI Fei, TANG Liping, YANG Xinmin . A kind of cone-convexity for set-valued maps and its scalarization[J]. Operations Research Transactions, 2016 , 20(4) : 21 -29 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.04.003

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