Paper Info
Title
An Extragradient-Based Alternating Direction Method for Convex Minimization
Abstract
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one of the two functions has an easy proximal mapping, the other function is smoothly convex but does not have an easy proximal mapping. Therefore, the classical alternating direction methods cannot be applied. To deal with the difficulty, we propose in this paper an alternating direction method based on . Under the assumption that the smooth function has a Lipschitz continuous gradient, we prove that the proposed method returns an -optimal solution within iterations. We apply the proposed method to solve a new statistical model called fused logistic regression. Our numerical experiments show that the proposed method performs very well when solving the test problems. We also test the performance of the proposed method through solving the lasso problem arising from statistics and compare the result with several existing efficient solvers for this problem; the results are very encouraging.
Year
DOI
Venue
2017
10.1007/s10208-015-9282-8
Foundations of Computational Mathematics
Keywords
Field
DocType
Alternating direction method,Extragradient,Iteration complexity,Lasso,Fused logistic regression,90C25,68Q25,62J05
Mathematical optimization,Mathematical analysis,Lasso (statistics),Algorithm,Proximal Gradient Methods,Regular polygon,Convex function,Lipschitz continuity,Statistical model,Smoothness,Convex optimization,Mathematics
Journal
Volume
Issue
ISSN
17
1
1615-3375
Citations 
PageRank 
References 
12
0.71
29
Authors
3
Name
Order
Citations
PageRank
Tianyi Lin114711.79
Shiqian Ma2106863.48
Shuzhong Zhang32808181.66