文献类型：期刊文献

英文题名：A NOTE ON THE KL PROPERTY OF THE AUGMENTED LAGRANGIAN FOR CONIC PROGRAMMING

作者：Wu, Jia[1];Zhang, Yi[2]

机构：[1]Dalian Univ Technol, Inst Operat Res & Control Theory, Sch Math Sci, Dalian 116024, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：21

期号：4

起止页码：2456

外文期刊名：JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

收录：;EI(收录号：20251218069807);WOS:【SCI-EXPANDED(收录号:WOS:001363862100001)】；

基金：The first author is supported by [National Key R&D Program of China under project No. 2022YFA1004000 and the Natural Science Foundation of China under No.12071055] . The corresponding author is supported by [National Natural Science Foundation of China under project No.12171153] .

语种：英文

外文关键词：Kurdyka- Lojasiewicz property; augmented Lagrangian; calmness; semi-isolated calmness; isolated calmness

摘要：. The relationship between the Kurdyka- Lojasiewicz (KL) property of the augmented Lagrangian for conic programming and various calmness conditions of its perturbed Karush-Kuhn-Tucker (KKT) system solution mapping is studied in this paper. We establish equivalences among calmness conditions -specifically calmness, semi-isolated calmness, and isolated calmness -between the perturbed KKT system solution mapping and the inverse of the subdifferential of the augmented Lagrangian. Under certain conditions, we demonstrate that calmness of the perturbed KKT system solution mapping implies the KL property of its augmented Lagrangian with an exponent of 1/2 at KKT points. Moreover, both semi-isolated calmness and isolated calmness of the KKT system solution mapping directly imply that the augmented Lagrangian satisfies the KL property with an exponent of 1/2 at KKT points. These results provide several approaches to determine the KL property of the augmented Lagrangian at KKT points, and their application is illustrated through examples.