Augmented Lagrangian Duality for Composite Optimization Problems

被引：5
|
作者：
Kan, Chao [1 ,2 ]
Song, Wen [1 ,2 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150006, Peoples R China
[2] Harbin Normal Univ, Sch Math & Sci, Harbin, Peoples R China
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 165卷 / 03期
关键词：
Augmented Lagrange multiplier; Moreau envelope; Duality; Second-order epi-derivative; OPTIMALITY CONDITIONS; CONVEX-FUNCTIONS; DERIVATIVES;
D O I：
10.1007/s10957-014-0640-5
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this paper, augmented Lagrangian duality is considered for composite optimization problems, and first- and second-order conditions for the existence of augmented Lagrange multipliers are presented. The analysis is based on the reformulation of the augmented Lagrangian in terms of the Moreau envelope functions and the technique of epi-convergence via the calculation of second-order epi-derivatives of the augmented Lagrangian. It is also proved that the second-order conditions for optimization problems with abstract constraints given in a form of set inclusions, obtained by Shapiro and Sun, can be derived directly from our general results.
引用
收藏
页码：763 / 784
页数：22
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