Well-posedness in vector optimization and scalarization results

In this paper, we give a survey on well-posedness notions of Tykhonov's type for vector optimization problems and the links between them with respect to the classification proposed by Miglierina, Molho and Rocca in [33]. We consider also the notions of extended well-posedness introduced by X.X. Huang ([19],[20]) in the nonparametric case to complete the hierchical structure characterizing these concepts. Finally we propose a review of some theoretical results in vector optimization mainly related to different notions of scalarizing functions, linear and nonlinear, introduced in the last decades, to simplify the study of various well-posedness properties.