Connectedness and Path Connectedness of Weak Efficient Solution Sets of Vector Optimization Problems via Nonlinear Scalarization Methods

Xin Xu and Yang Dong Xu
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Xin Xu: College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Yang Dong Xu: College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Mathematics, 2019, vol. 7, issue 10, 1-10

Abstract: The connectedness and path connectedness of the solution sets to vector optimization problems is an important and interesting study in optimization theories and applications. Most papers involving the direction established the connectedness and connectedness for the solution sets of vector optimization problems or vector equilibrium problems by means of the linear scalarization method rather than the nonlinear scalarization method. The aim of the paper is to deal with the connectedness and the path connectedness for the weak efficient solution set to a vector optimization problem by using the nonlinear scalarization method. Firstly, the union relationship between the weak efficient solution set to the vector optimization problem and the solution sets to a series of parametric scalar minimization problems, is established. Then, some properties of the solution sets of scalar minimization problems are investigated. Finally, by using the union relationship, the connectedness and the path connectedness for the weak efficient solution set of the vector optimization problem are obtained.

Keywords: vector optimization problem; nonlinear scalarization; connectedness; path connectedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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