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Levitin-polyakwell-posedness for set-valued optimization problems with constraints

Chen Jiawei (Southwest University, School of Mathematics and Statistics, Chongqing, China)
Cho Yeol Je (Gyeongsang National University, Department of Mathematics Education and the RINS, Jinju, Korea + King Abdulaziz University, Department of Mathematics, Jeddah, Saudi Arabia)
Ou Xiaoqing (Chongqing College of Humanities, Science & Technology, College of Management, Chongqing, China)

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 wellposedness 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.

Keywords: Set-valued optimization problems with constraints, Levitin-Polyak well-posedness, metric characterization, System of general variational inclusion, System of general variational disclusion