In this paper, Levitin-Polyak well-posedness for generalized quasi-variational inclusion and disclusion problems are introduced and studied. Necessary and sufficient conditions for Levitin-Polyak well-posedness of these problems are proved. Moreover, Levitin-Polyak well-posedness for optimization problems with generalized quasi-variational inclusion problems, generalized quasi-variational disclusion problems and scalar generalized quasi-equilibrium problems as constraints are also given under some suitable conditions.
"LEVITIN-POLYAK WELL-POSEDNESS FOR GENERALIZED QUASI-VARIATIONAL INCLUSION AND DISCLUSION PROBLEMS AND OPTIMIZATION PROBLEMS WITH CONSTRAINTS." Taiwanese J. Math. 16 (1) 237 - 257, 2012. https://doi.org/10.11650/twjm/1500406539