Scalarization and pointwise well-posedness in vector optimization problems

Authors:
Gang Xiao;Hong Xiao;Sanyang Liu
Affiliations:
Department of Math and Information Technology, Hanshan Normal University, Chaozhou, People's Republic of China 521041;Ceramic college, Hanshan Normal University, Chaozhou, People's Republic of China 521041;Department of Applied Mathematics, Xidian University, Xi'an, People's Republic of China 710071
Venue:
Journal of Global Optimization
Year:
2011

Citing 5
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Abstract

The aim of this paper is applying the scalarization technique to study some properties of the vector optimization problems under variable domination structure. We first introduce a nonlinear scalarization function of the vector-valued map and then study the relationships between the vector optimization problems under variable domination structure and its scalarized optimization problems. Moreover, we give the notions of DH-well-posedness and B-well-posedness under variable domination structure and prove that there exists a class of scalar problems whose well-posedness properties are equivalent to that of the original vector optimization problem.