Levitin--Polyak Well-Posedness for Set-Valued Optimization Problems With Constraints

Jiawei Chen, Yeol Je Cho, Xiaoqing Ou

In this paper, Levitin--Polyak well-posedness for set-valued optimization problems with constraints is introduced. Some sufficient and necessary conditions for the Levitin--Polyak well-posedness of these problems are established under some suitable conditions. The equivalence between the well-posedness of optimization problems with constraints and the existence and uniqueness of their solutions are proved. Finally, we give some examples to illustrate the presented results.