In this paper, we consider Levitin-Polyak-type well-posedness for a general constrained optimization problem. We introduce generalized Levitin-Polyak well-posedness and strongly generalized Levitin-Polyak well-posedness. Necessary and sufficient conditions for these types of well-posedness are given. Relations among these types of well-posedness are investigated. Finally, we consider convergence of a class of penalty methods and a class of augmented Lagrangian methods under the assumption of strongly generalized Levitin-Polyak well-posedness.
- Constrained optimization
- Generalized Levitin-Polyak well-posedness
- Generalized minimizing sequence
- Penalty-type methods
ASJC Scopus subject areas
- Theoretical Computer Science