Abstract
It is well-known that the primal quadratic growth condition of the classical augmented Lagrangian around a local minimizer can be obtained under the second-order sufficient optimality condition. In this paper, we show that those conditions are indeed equivalent. Moreover, we prove that the primal quadratic growth condition of the sharp augmented Lagrangian around a local minimizer is in fact equivalent to the weak second-order sufficient optimality condition. In addition, we present some secondary results involving the sharp augmented Lagrangian.
Acknowledgments
The author thank the two referees for their useful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author.