Abstract
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.
Acknowledgements
We would like to express our gratitude to the anonymous referees for their helpful comments on the first version of this paper.
Notes
No potential conflict of interest was reported by the authors.