An Inexact Linearized Augmented Lagrangian Method for the Linearly Composite Convex Programming

被引：0
作者：
Zhu, Ting-Ting [1 ]
He, Xin [2 ]
Fang, Ya-Ping [1 ]
机构：
[1] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China
[2] Xihua Univ, Sch Sci, Chengdu 610039, Sichuan, Peoples R China
来源：
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH | 2025年
基金：
中国国家自然科学基金;
关键词：
Linear equality constrained composite convex programming; inexact linearized augmented Lagrangian method; customized linearized augmented Lagrangian method; convergence rate; MINIMIZATION;
D O I：
10.1142/S0217595925500174
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：
We propose an inexact linearized augmented Lagrangian method for the linear equality constrained convex programming, for which the objective function has a "nonsmooth + smooth" composite structure. We show that both the objective error and the constraint gap associated with the proposed algorithm enjoy an O(1/k) nonergodic convergence rate. By choosing a specific proximal matrix, we drive a customized linearized augmented Lagrangian method for the problem, where the subproblem can be solved by means of the proximal mapping of a convex function. Finally, we demonstrate the efficiency of the proposed algorithms by two numerical experiments.
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页数：19
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