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.

为解决具有特殊结构的大规模优化问题，将发展新的高效计算算法。结构化非线性优化在图像处理、最优控制、大数据随机学习等现代应用中发挥着重要作用。该项目中开发的算法将以更强大、更快的方式提供解决方案，并将公开提供，以使优化和计算数据科学社区受益。本项目所支持的学生将有很好的跨学科研究机会。目前解决结构化优化问题的方法往往需要根据问题结构求解一系列子问题。该项目旨在开发有效的方法和软件，允许不精确地解决其子问题，同时在理论上仍然保证全局收敛，并保持与需要精确解决子问题的相应方法相同或几乎相同的计算复杂性。特别是，研究者将开发（I）可分离凸优化的乘子的不精确交替方向方法的框架，其中子问题被解决到相对于整个问题KKT误差的准确度;（II）复合优化的不精确随机梯度方法，它结合了（加速）邻近梯度法和随机方差减少技术;（三）不准确的主动性-该奖项反映了NSF的法定使命，并通过使用基金会的学术价值和更广泛的影响审查标准。

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

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

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