Scalarization and pointwise well-posedness in vector optimization problems

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.