Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (3): 62-68.doi: 10.16088/j.issn.1001-6600.2020091101

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Connectedness of Weakly Effective Solution Sets for Convex Vector Optimization Problems

ZHONG Liming, FAN Jianghua*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2020-09-11 Revised:2020-10-12 Published:2021-05-13

Abstract: The connectedness of solution sets for vector optimization problems is studied in this paper. By means of the scalarization method, the connectedness of weakly efficient solutions sets for convex vector optimization problems on the unbounded, closed and convex sets are discussed. When the vector valued mapping is cone-lowersemicontinuous and cone-convex, the mapping of solution sets is proved to be upper semicontinuous and the connectedness of solution set by using the connectedness of the compact and convex base of the polar cone is established. When the vector valued mapping is cone-lowersemicontinuous and strictly cone-convex, the path-connectedness of solution sets of convex vector optimization problems are obtained. Furthermore, the connectedness of weakly efficient solutions sets of composite multiobjective optimization problems and the connectedness of solution sets of affine vector variational inequality problems are obtained.

Key words: vector optimization problem, weakly efficient solutions, nonempty and compact set, connectedness, path-connectedness

CLC Number: 

  • O224.1
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