Optimization Methods for Nonconvex Structured Optimization

非凸结构化优化的优化方法

• 批准号: 2110722
• 负责人: Hongchao Zhang
• 金额: $ 15万
• 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: 2021
• 资助国家: 美国
• 起止时间: 2021-07-15 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110722&HistoricalAwards=false
• 关键词: Optimization; Methods; Nonconvex; Structured

This project will advance fundamental algorithmic theory and software tools for solving optimization problems with wide applications in science, engineering and industry. Specifically, the project will be in the area of structured nonconvex nonlinear optimization, a critical component in many modern applications ranging from signal/image processing, real-time optimal control to stochastic learning. The project aims to develop algorithms with focus on the following features: speed, problem dependence, and ease of use for researchers in both optimization and computational data science community. Students will be involved and will have opportunities for interdisciplinary research. Software will be developed.This project will develop theoretically strong and numerically efficient algorithms as well as the software for solving nonconvex structured optimization. These algorithms will solve the subproblems inexactly with guaranteed global convergence as well as feature an optimal computational complexity when the problem features convexity structure. The algorithms will be based on recent work on proximal and stochastic gradient methods for structured composite minimization, inexact alternating direction multiplier methods (ADMM) for separable convex/nonconvex optimization and active set methods for polyhedral constrained optimization. In addition, second-order techniques for accelerating the convergence will be also explored.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.

该项目将为解决在科学、工程和工业中广泛应用的优化问题提供基本的算法理论和软件工具。具体地说，该项目将在结构化非凸非线性优化领域，这是从信号/图像处理、实时最优控制到随机学习等许多现代应用中的关键组件。该项目旨在开发专注于以下特征的算法：速度、问题依赖性和易用性，供优化和计算数据科学界的研究人员使用。学生将参与并将有机会进行跨学科研究。将开发软件。该项目将开发理论上强大的和数值高效的算法以及求解非凸结构优化的软件。当问题具有凸性结构时，这些算法将在保证全局收敛的前提下解决不精确的子问题，并具有最优的计算复杂度。这些算法将基于最近关于结构组合极小化的近似法和随机梯度法、可分离凸/非凸优化的不精确交替方向乘子法(ADMM)和多面体约束优化的有效集方法的最新工作。此外，还将探索加速融合的二阶技术。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

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

On the acceleration of the Barzilai–Borwein method

论 BarzilaiâªBorwein 方法的加速

• DOI: 10.1007/s10589-022-00349-z
• 发表时间: 2020-01
• 期刊: Computational Optimization and Applications
• 影响因子: 2.2
• 作者: Yakui Huang;Yu-Hong Dai;Xin-Wei Liu;Hongchao Zhang
• 通讯作者: Hongchao Zhang

An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems

• DOI: 10.1007/s10957-022-02152-6
• 发表时间: 2022-12
• 期刊: Journal of Optimization Theory and Applications
• 影响因子: 1.9
• 作者: Jingyong Tang;Jinchuan Zhou;Hongchao Zhang

Unified linear convergence of first-order primal-dual algorithms for saddle point problems

鞍点问题一阶原对偶算法的统一线性收敛

• DOI: 10.1007/s11590-021-01832-y
• 发表时间: 2022-01
• 期刊: Optimization Letters
• 影响因子: 1.6
• 作者: Fan Jiang;Zhongming Wu;Xingju Cai;Hongchao Zhang
• 通讯作者: Hongchao Zhang

Golden Ratio Primal-Dual Algorithm with Linesearch

• DOI: 10.1137/21m1420319
• 发表时间: 2021-05
• 期刊: SIAM J. Optim.
• 作者: Xiaokai Chang;Junfeng Yang;Hongchao Zhang