This paper investigates the necessary and sufficient conditions for the generalized D 0 -well-posedness of set optimization problems and the generalized well-posedness of scalar optimization problems. Based on the partial order relation defined by the Minkowski difference, a new class of nonlinear scalarization functions is introduced. Through strict derivation of the monotonicity of this function and in combination with the intrinsic characteristics of the partial order relation, the characterization of weakly minimal solutions of set optimization problems under certain conditions and the derivation of well-posedness results are accomplished. The scalarization equivalent conditions for weakly minimal solutions of set optimization problems are obtained, and it is proved that a set optimization problem is generalized D〖TX-〗 0 -well-posed if and only if the scalarization problem is generalized well-posed. The results of this paper enrich the related achievements of scalarization methods and well-posedness theory for set optimization problems.