Abstract
We propose definitions of well-posedness under perturbation in terms of suitable asymptotically solving sequences, not embedding a given problem into a parameterized family. When considering in detail quasi-equilibrium and quasi-optimization problems as well as optimization problems with equilibrium constraints, we establish sufficient conditions for both well-posedness and unique well-posedness. For cases with noncompact underlying sets of constraints, measures of noncompactness are employed. We provide numerous examples to ensure the essentialness of the assumptions imposed in the obtained results.
Acknowledgment
The authors are very grateful to the Editors and Referees for their valuable remarks and suggestions that helped us significantly improve the paper. For the first and the last authors, this is a result of the project under Grant number B2021-TCT-02 supported by the Ministry of Education and Training of Viet Nam.