New Analysis of an Away-Step Frank–Wolfe Method for Minimizing Log-Homogeneous Barriers

数学 同种类的 数理经济学 数学优化 应用数学 牙石(牙科) 组合数学 医学 牙科
作者
Renbo Zhao
出处
期刊:Mathematics of Operations Research [Institute for Operations Research and the Management Sciences]
标识
DOI:10.1287/moor.2023.0281
摘要

We present and analyze an away-step Frank–Wolfe method for the convex optimization problem [Formula: see text], where f is a θ-logarithmically homogeneous self-concordant barrier, [Formula: see text] is a linear operator that may be noninvertible, [Formula: see text] is a linear function, and [Formula: see text] is a nonempty polytope. The applications of primary interest include D-optimal design, inference of multivariate Hawkes processes, and total variation-regularized Poisson image deblurring. We establish affine-invariant and norm-independent global linear convergence rates of our method in terms of both the objective gap and the Frank–Wolfe gap. When specialized to the D-optimal design problem, our results settle a question left open since Ahipasaoglu et al. [Ahipasaoglu SD, Sun P, Todd MJ (2008) Linear convergence of a modified Frank–Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optim. Methods Software 23(1):5–19]. We also show that the iterates generated by our method will land on and remain in a face of [Formula: see text] within a bounded number of iterations, which can lead to improved local linear convergence rates (for both the objective gap and the Frank–Wolfe gap). We conduct numerical experiments on D-optimal design and inference of multivariate Hawkes processes, and our results not only demonstrate the efficiency and effectiveness of our method compared with other principled first-order methods but also, corroborate our theoretical results quite well. Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA9550-22-1-0356].
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
1秒前
赘婿应助面包采纳,获得10
1秒前
1秒前
Yanan_Z发布了新的文献求助10
1秒前
量子星尘发布了新的文献求助10
1秒前
阿吉完成签到,获得积分10
2秒前
QH应助LucienS采纳,获得10
3秒前
穆振家完成签到,获得积分10
4秒前
米奇马奥斯完成签到,获得积分10
4秒前
5秒前
7秒前
D1fficulty发布了新的文献求助10
8秒前
8秒前
领导范儿应助出门右转采纳,获得10
8秒前
麻果发布了新的文献求助10
9秒前
10秒前
Www完成签到,获得积分10
10秒前
核桃发布了新的文献求助10
11秒前
zzzzzy发布了新的文献求助10
11秒前
12秒前
宇文书翠完成签到,获得积分10
13秒前
XHH1994发布了新的文献求助10
13秒前
123444发布了新的文献求助10
13秒前
13秒前
大王完成签到,获得积分10
13秒前
香蕉晓曼完成签到,获得积分10
14秒前
psybrain9527完成签到,获得积分10
15秒前
gulllluuuukk完成签到,获得积分10
15秒前
典雅的丹寒完成签到,获得积分10
16秒前
wyvern114完成签到,获得积分10
16秒前
16秒前
所所应助好好学习采纳,获得10
17秒前
大王发布了新的文献求助10
17秒前
陈隆发布了新的文献求助10
18秒前
DijiaXu应助chili采纳,获得10
18秒前
我是老大应助chili采纳,获得10
18秒前
李健应助小董采纳,获得10
19秒前
19秒前
小核桃完成签到,获得积分10
19秒前
连仁兄发布了新的文献求助10
20秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
Cognitive Neuroscience: The Biology of the Mind 1000
Technical Brochure TB 814: LPIT applications in HV gas insulated switchgear 1000
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 500
Picture Books with Same-sex Parented Families: Unintentional Censorship 500
Nucleophilic substitution in azasydnone-modified dinitroanisoles 500
不知道标题是什么 500
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3970172
求助须知:如何正确求助?哪些是违规求助? 3514982
关于积分的说明 11176568
捐赠科研通 3250212
什么是DOI,文献DOI怎么找? 1795198
邀请新用户注册赠送积分活动 875702
科研通“疑难数据库(出版商)”最低求助积分说明 805004