Acceleration Techniques for Lower-Order Algorithms in Nonlinear Optimization

非线性优化中低阶算法的加速技术

• 批准号: 1522654
• 负责人: Hongchao Zhang
• 金额: $ 17.78万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522654&HistoricalAwards=false
• 关键词: Acceleration; Techniques; Lower; Order; Algorithms

This project focuses on developing efficient innovative acceleration techniques and their underlying theories for the algorithms in nonlinear optimization. The acceleration techniques and algorithms developed in this project will have broad impact in many areas of computational science, including imaging/signal processing, optimal control, computer vision, petroleum engineering, topology optimization, and electronic structure computations. The algorithms developed in this research will be made publicly available on the web and will be applied in solving various computational problems. In addition, the student involved in this project will have excellent opportunities to participate in interdisciplinary research.The research will include developing subspace techniques for nonlinear conjugate gradient method and accelerated nonlinear conjugate gradient methods with theoretically guaranteed optimal global complexity. A framework of inexact alternating direction method of multipliers (ADMM) will also be developed, in which multiple steps are allowed to solve the subproblem to an adaptive accuracy, while still maintaining global convergence even when the problem has more than two blocks. The project will also study acceleration strategies for gradient based stochastic optimization. In particular, adaptive strategies for choosing sample points and extracting quasi-Newton information based on the obtained stochastic information will be explored. In addition, a novel dual active set approach will be developed for solving smooth large-scale nonlinear optimization. For example, in projection on polyhedra, an algorithm can be developed to approximately identify the active linear constraints, while an asymptotically faster algorithm can be used to compute a high accuracy solution.

该项目着重于开发有效的创新加速技术及其对非线性优化算法的基本理论。该项目中开发的加速技术和算法将在许多计算科学领域都产生广泛的影响，包括成像/信号处理，最佳控制，计算机视觉，石油工程，拓扑优化和电子结构计算。本研究中开发的算法将在网络上公开可用，并将应用于解决各种计算问题。此外，参与该项目的学生将有极好的机会参与跨学科研究。该研究将包括开发针对非线性共轭梯度方法的子空间技术以及具有理论上保证最佳全球复杂性的非线性非线性共轭梯度方法。还将开发一个不精确的交替方向方法（ADMM）的框架，其中允许多个步骤将子问题求解至自适应精度，同时即使问题有两个以上的块，也仍然保持全局收敛。该项目还将研究基于梯度随机优化的加速策略。特别是，将探索基于获得的随机信息选择样品点并提取准牛顿信息的自适应策略。此外，将开发一种新型的双重主动设置方法来解决平滑的大规模非线性优化。例如，在Polyhedra的投影中，可以开发出一种算法以近似识别活动线性约束，而渐近更快的算法则可以用于计算高精度解决方案。

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

A Nonmonotone Smoothing Newton Algorithm for Weighted Complementarity Problem

• DOI: 10.1007/s10957-021-01839-6
• 发表时间: 2021-03
• 期刊: Journal of Optimization Theory and Applications
• 影响因子: 1.9
• 作者: Jingyong Tang;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