Scalarization of Levitin–Polyak well-posed set optimization problems

The aim of this paper is to study Levitin–Polyak (LP in short) well-posedness for set optimization problems. We define the global notions of metrically well-setness and metrically LP well-setness and the pointwise notions of LP well-posedness, strongly DH-well-posedness and strongly B-well-posedness for set optimization problems. Using a scalarization function defined by means of the point-to-set distance, we characterize the LP well-posedness and the metrically well-setness of a set optimization problem through the LP well-posedness and the metrically well-setness of a scalar optimization problem, respectively.