On Hadamard well-posedness and convergence in set optimization

The purpose of this article is to explore the Hadamard well-posedness in the context of set optimization problems. Initially, we introduce two novel definitions of Hadamard well-posedness specifically tailored for set optimization scenarios. Subsequently, we establish a relationship between these two definitions. Furthermore, we outline sufficient conditions that ensure the Hadamard well-posedness of set optimization problems. Additionally, by utilizing the scalarization technique, we establish further sufficient conditions for Hadamard well-posedness in set optimization problems. Finally, we discuss the convergence of m-minimal approximate solution sets for the set optimization problem.