학술논문
A highly efficient semismooth Newton augmented Lagrangian method for solving lasso problems.
Document Type
Journal
Author
Li, Xudong (1-PRIN-ORF) AMS Author Profile; Sun, Defeng (PRC-HP-AM) AMS Author Profile; Toh, Kim-Chuan (SGP-SING) AMS Author Profile
Source
Subject
65 Numerical analysis -- 65K Mathematical programming, optimization and variational techniques
65K05Mathematical programming methods
90Operations research, mathematical programming -- 90C Mathematical programming
90C06Large-scale problems
90C25Convex programming
90C31Sensitivity, stability, parametric optimization
65K05
90
90C06
90C25
90C31
Language
English
Abstract
In this paper, the authors introduce an inexact augmented Lagrangian method for solving general convex composite optimization problems. To make this method effective, they propose a semismooth Newton algorithm for solving the subproblems in the augmented Lagrangian method. Global convergence results are stated, and numerical results show the efficiency and the robustness of their algorithm, where second-order information plays an important role. Comparisons are also made with other methods.