Operator Splitting Methods: Certificates and Second-Order Acceleration
算子拆分方法:证书和二阶加速
基本信息
- 批准号:1720237
- 负责人:
- 金额:$ 20.5万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-07-01 至 2020-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research project is centered on development of improved numerical algorithms for application to large-scale systems that include, for example, signal/image/video reconstruction and processing, bioinformatics, and automated learning or mining of information from very large data sets. Operator splitting is a class of methods that decomposes a difficult problem into simple sub-problems. Within the past decade, operator splitting methods gained popularity due to the growing demand to handle ever-larger models. For example, signal processing and machine learning applications often have multiple parts that are easy to handle separately but are very challenging when combined. Ideas from operator splitting have led to efficient algorithms for broad classes of objective functions that are used to define the underlying systems. There is still, however, much to be done to handle complex situations. Through further development of operator splitting techniques, this research has the potential to provide efficient and stable approaches to solve a yet wider class of challenging problems. The project also includes educational impact through the development of courses, presentation of seminars, and graduate student training opportunities.The principal investigator intends to design and implement algorithms that improve the speed and stability of operator splitting methods. This project aims to extend the principle of operator splitting in two ways. First, operator splitting algorithms will be introduced that recognize infeasible and feasible-but-unbounded optimization problems, as well as those that have finite optimal values but unattainable solutions. Such pathological problems are not rare and cripple existing techniques. The new algorithms will address these pathologies and make future solvers more robust. Second, by incorporating second-order information in a novel fashion, the project will address two significant drawbacks of operator splitting algorithms. These are the slow tail convergence, and the sensitivity to severe problem conditions. Techniques to ensure global convergence will be developed. Because operator splitting is a high-level abstraction, the results of the project will apply to a broad range of numerical methods that arise in science and engineering.
该研究项目的重点是开发适用于大规模系统的改进数值算法,例如,信号/图像/视频重建和处理,生物信息学以及从非常大的数据集中自动学习或挖掘信息。算子分裂是一类将困难问题分解为简单子问题的方法。 在过去的十年中,运营商分裂的方法得到普及,由于不断增长的需求,以处理越来越大的模型。例如,信号处理和机器学习应用通常有多个部分,这些部分很容易单独处理,但组合起来就非常具有挑战性。算子分裂的思想已经导致了用于定义底层系统的广泛类别的目标函数的有效算法。然而,在处理复杂局势方面仍有许多工作要做。通过算子分裂技术的进一步发展,这项研究有可能提供有效和稳定的方法来解决更广泛的一类具有挑战性的问题。该项目还包括通过课程开发,研讨会的介绍和研究生培训机会的教育影响。首席研究员打算设计和实现提高运算符分裂方法的速度和稳定性的算法。该项目旨在以两种方式扩展算子分裂的原理。首先,将介绍算子分裂算法,该算法识别不可行和可行但无界的优化问题,以及那些具有有限的最优值但无法达到的解决方案。这种病理问题并不罕见,并削弱了现有的技术。新算法将解决这些问题,并使未来的求解器更加强大。其次,通过以一种新颖的方式结合二阶信息,该项目将解决算子分裂算法的两个显著缺点。这些是缓慢的尾部收敛,以及对严重问题条件的敏感性。将开发确保全球趋同的技术。由于算子分裂是一个高层次的抽象,该项目的结果将适用于科学和工程中出现的广泛的数值方法。
项目成果
期刊论文数量(21)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A new use of Douglas–Rachford splitting for identifying infeasible, unbounded, and pathological conic programs
- DOI:10.1007/s10107-018-1265-5
- 发表时间:2018-04
- 期刊:
- 影响因子:2.7
- 作者:Yanli Liu;Ernest K. Ryu;W. Yin
- 通讯作者:Yanli Liu;Ernest K. Ryu;W. Yin
On Markov Chain Gradient Descent
- DOI:
- 发表时间:2018-09
- 期刊:
- 影响因子:0
- 作者:Tao Sun;Yuejiao Sun;W. Yin
- 通讯作者:Tao Sun;Yuejiao Sun;W. Yin
On Unbounded Delays in Asynchronous Parallel Fixed-Point Algorithms
- DOI:10.1007/s10915-017-0628-z
- 发表时间:2016-09
- 期刊:
- 影响因子:2.5
- 作者:Robert Hannah;W. Yin
- 通讯作者:Robert Hannah;W. Yin
Decentralized Accelerated Gradient Methods With Increasing Penalty Parameters
- DOI:10.1109/tsp.2020.3018317
- 发表时间:2018-10
- 期刊:
- 影响因子:5.4
- 作者:Huan Li;Cong Fang;W. Yin;Zhouchen Lin
- 通讯作者:Huan Li;Cong Fang;W. Yin;Zhouchen Lin
Tight coefficients of averaged operators via scaled relative graph
通过缩放相对图计算平均算子的紧系数
- DOI:10.1016/j.jmaa.2020.124211
- 发表时间:2020
- 期刊:
- 影响因子:1.3
- 作者:Huang, Xinmeng;Ryu, Ernest K.;Yin, Wotao
- 通讯作者:Yin, Wotao
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Wotao Yin其他文献
ExtraPush for consensus optimization with convex differentiable objective functions over a directed network
ExtraPush 通过有向网络上的凸可微目标函数实现共识优化
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0.9
- 作者:
Jinshan Zeng;Wotao Yin - 通讯作者:
Wotao Yin
Learning Collaborative Sparsity Structure via Nonconvex Optimization for Feature Recognition
通过非凸优化学习协作稀疏结构进行特征识别
- DOI:
10.1109/tii.2017.2777144 - 发表时间:
2018-10 - 期刊:
- 影响因子:12.3
- 作者:
Zhaohui Du;Xuefeng Chen;Han Zhang;Ruqiang Yan;Wotao Yin - 通讯作者:
Wotao Yin
One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
l1 综合和 l1 分析最小化的解决方案唯一性和鲁棒性的一个条件
- DOI:
10.1007/s10444-016-9467-y - 发表时间:
2013-04 - 期刊:
- 影响因子:1.7
- 作者:
Hui Zhang;Ming Yan;Wotao Yin - 通讯作者:
Wotao Yin
Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs
(混合整数)二次规划的图神经网络的表达能力
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Ziang Chen;Xiaohan Chen;Jialin Liu;Xinshang Wang;Wotao Yin - 通讯作者:
Wotao Yin
Decentralized jointly sparse signal recovery by reweighted lq minimization
通过重新加权 lq 最小化分散式联合稀疏信号恢复
- DOI:
- 发表时间:
- 期刊:
- 影响因子:5.4
- 作者:
Qing Ling;Zaiwen Wen;Wotao Yin - 通讯作者:
Wotao Yin
Wotao Yin的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Wotao Yin', 18)}}的其他基金
EAGER- DynamicData: Novel Approaches for Optimization, Control, and Learning in Distributed Networks
EAGER-DynamicData:分布式网络中优化、控制和学习的新方法
- 批准号:
1462397 - 财政年份:2015
- 资助金额:
$ 20.5万 - 项目类别:
Standard Grant
Computation of Large-Scale, Multi-Dimensional Sparse Optimization Problems
大规模、多维稀疏优化问题的计算
- 批准号:
1317602 - 财政年份:2013
- 资助金额:
$ 20.5万 - 项目类别:
Continuing Grant
CAREER: Optimizations for Sparse Solutions and Applications
职业:稀疏解决方案和应用程序的优化
- 批准号:
1349855 - 财政年份:2013
- 资助金额:
$ 20.5万 - 项目类别:
Continuing Grant
CAREER: Optimizations for Sparse Solutions and Applications
职业:稀疏解决方案和应用程序的优化
- 批准号:
0748839 - 财政年份:2008
- 资助金额:
$ 20.5万 - 项目类别:
Continuing Grant
相似海外基金
Analysis, design, and implementation of novel high-order operator splitting methods
新型高阶算子分裂方法的分析、设计与实现
- 批准号:
574878-2022 - 财政年份:2022
- 资助金额:
$ 20.5万 - 项目类别:
University Undergraduate Student Research Awards
Temporal Splitting Methods for Multiscale Problems
多尺度问题的时间分裂方法
- 批准号:
2208498 - 财政年份:2022
- 资助金额:
$ 20.5万 - 项目类别:
Continuing Grant
Splitting methods in optimization: Beyond consistency and convexity.
优化中的分割方法:超越一致性和凸性。
- 批准号:
RGPIN-2019-04803 - 财政年份:2022
- 资助金额:
$ 20.5万 - 项目类别:
Discovery Grants Program - Individual
Splitting methods in optimization: Beyond consistency and convexity.
优化中的分割方法:超越一致性和凸性。
- 批准号:
RGPIN-2019-04803 - 财政年份:2021
- 资助金额:
$ 20.5万 - 项目类别:
Discovery Grants Program - Individual
Analysis, design, and implementation of novel high-order operator splitting methods
新型高阶算子分裂方法的分析、设计与实现
- 批准号:
564781-2021 - 财政年份:2021
- 资助金额:
$ 20.5万 - 项目类别:
University Undergraduate Student Research Awards
Splitting methods in optimization: Beyond consistency and convexity.
优化中的分割方法:超越一致性和凸性。
- 批准号:
RGPIN-2019-04803 - 财政年份:2020
- 资助金额:
$ 20.5万 - 项目类别:
Discovery Grants Program - Individual
Analysis, design, and implementation of novel high-order operator splitting methods
新型高阶算子分裂方法的分析、设计与实现
- 批准号:
551586-2020 - 财政年份:2020
- 资助金额:
$ 20.5万 - 项目类别:
University Undergraduate Student Research Awards
Splitting methods in optimization: Beyond consistency and convexity.
优化中的分割方法:超越一致性和凸性。
- 批准号:
RGPIN-2019-04803 - 财政年份:2019
- 资助金额:
$ 20.5万 - 项目类别:
Discovery Grants Program - Individual
Splitting methods in optimization: Beyond consistency and convexity.
优化中的分割方法:超越一致性和凸性。
- 批准号:
DGECR-2019-00314 - 财政年份:2019
- 资助金额:
$ 20.5万 - 项目类别:
Discovery Launch Supplement
Splitting methods for nonconvex and inconsistent problems
非凸和不一致问题的分裂方法
- 批准号:
502917-2017 - 财政年份:2019
- 资助金额:
$ 20.5万 - 项目类别:
Postdoctoral Fellowships