Scalarization method for Levitin-Polyak well-posedness of vectorial optimization problems

In this paper, we develop a method of study of Levitin-Polyak well-posedness notions for vector valued optimization problems using a class of scalar optimization problems. We first introduce a non-linear scalarization function and consider its corresponding properties. We also introduce the Furi-Vignoli type measure and Dontchev-Zolezzi type measure to scalar optimization problems and vectorial optimization problems, respectively. Finally, we construct the equivalence relations between the Levitin-Polyak well-posedness of scalar optimization problems and the vectorial optimization problems.