Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions. (2nd January 2022)

• Record Type: Journal Article
• Authors: Fernández, Damián
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 97
• Page End: 115
• Publication Date: 2022-01-02
• Subjects: Augmented Lagrangian -- sharp augmented Lagrangian -- second-order sufficient optimality condition -- weak second-order sufficient optimality condition; 90C46 -- 90C30 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1804567
• Languages: English
• ISSNs: 0233-1934

Abstract

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.