Inexact Optimization Methods for Structured Nonlinear Optimization

结构化非线性优化的不精确优化方法

• 批准号: 1819161
• 负责人: Hongchao Zhang
• 金额: $ 20万
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-15 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1819161&HistoricalAwards=false
• 关键词: Inexact; Optimization; Methods; Structured; Nonlinear

New efficient computational algorithms will be developed for solving large-scale optimization problems with particular structure. Structured nonlinear optimization has played a central role in various modern applications ranging from image processing, optimal control to stochastic learning in big data area. The algorithms developed in the project will provide solutions in a more robust and faster way, and will be made publicly available to benefit both optimization and computational data science community. The student supported in this project will have excellent opportunities for interdisciplinary research.The current methods for solving structured optimization problems often need to solve a sequence of subproblems according to the problem structure. This project aims to develop efficient methods and software that allow to solve their subproblems inexactly while still theoretically guarantee the global convergence and maintain the same or almost the same computational complexity of the corresponding methods that require exact solve of the subproblems. In particular, the investigator will develop (I) a framework of inexact alternating direction methods of multipliers for separable convex optimization, where the subproblem is solved to the accuracy relative to the whole problem KKT error; (II) inexact stochastic gradient methods for the composite optimization, which combines the(accelerated) proximal gradient methods and stochastic variance reduction techniques; (III) inexact active-set algorithms for polyhedral constrained nonlinear optimization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

将开发新的高效计算算法，以解决特定结构的大规模优化问题。结构化的非线性优化在从图像处理，最佳控制到大数据领域的随机学习的各种现代应用中发挥了核心作用。项目中开发的算法将以更强大，更快的方式提供解决方案，并将公开使用以使优化和计算数据科学界受益。该项目中支持的学生将为跨学科研究提供极好的机会。解决结构化优化问题的当前方法通常需要根据问题结构解决一系列子问题。该项目旨在开发有效的方法和软件，以使其子问题不确定地解决，同时在理论上仍然保证了全局收敛性，并保持相同或几乎相同的计算复杂性，这些计算复杂性需要准确求解子问题的相应方法。特别是，研究者将开发（i）一个不精确的交替方向方法，用于可分离凸优化，其中子问题与整个问题KKT误差相对于整个问题的准确性； （ii）复合优化的不精确随机梯度方法，该方法结合了（加速）近端梯度方法和随机方差降低技术； （iii）多面体约束非线性优化的不精确活动算法。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。

项目成果

Inexact alternating direction methods of multipliers for separable convex optimization

• DOI: 10.1007/s10589-019-00072-2
• 发表时间: 2019-02
• 期刊: Computational Optimization and Applications
• 影响因子: 2.2
• 作者: W. Hager;Hongchao Zhang

Generalized Uniformly Optimal Methods for Nonlinear Programming

• DOI: 10.1007/s10915-019-00915-4
• 发表时间: 2019-06-01
• 期刊: JOURNAL OF SCIENTIFIC COMPUTING
• 影响因子: 2.5
• 作者: Ghadimi, Saeed;Lan, Guanghui;Zhang, Hongchao
• 通讯作者: Zhang, Hongchao

Convergence rates for an inexact ADMM applied to separable convex optimization

• DOI: 10.1007/s10589-020-00221-y
• 发表时间: 2020-01
• 期刊: Computational Optimization and Applications
• 影响因子: 2.2
• 作者: W. Hager;Hongchao Zhang

On the Asymptotic Convergence and Acceleration of Gradient Methods

• DOI: 10.1007/s10915-021-01685-8
• 发表时间: 2019-08
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Yakui Huang;Yuhong Dai;Xinwei Liu;Hongchao Zhang

A Derivative-Free Geometric Algorithm for Optimization on a Sphere

• DOI: 10.4208/csiam-am.2020-0026
• 发表时间: 2020-06
• 期刊: CSIAM Transactions on Applied Mathematics
• 作者: Yannan Chen