Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions

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.

Keywords:

• Augmented Lagrangian
• sharp augmented Lagrangian
• second-order sufficient optimality condition
• weak second-order sufficient optimality condition

AMS CLASSIFICATIONS:

• 90C46
• 90C30
• 65K05

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.

Additional information

Funding

This work was partially supported by CONICET [grant number PIP-11220150100500CO] and Secretaria de Ciencia y Tecnología - Universidad Nacional de Córdoba [grant number PID-33620180100326CB].