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; 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.

该项目将推进基本算法理论和软件工具，以解决科学，工程和行业中广泛应用的优化问题。具体而言，该项目将位于结构化的非凸非线性优化的领域，这是许多现代应用程序中的关键组件，从信号/图像处理，实时最佳控制到随机学习。该项目旨在开发算法，重点关注以下功能：速度，问题依赖性以及优化和计算数据科学界的研究人员的易用性。学生将参与其中，并有跨学科研究的机会。将开发软件。此项目将开发理论上强，有效的算法，以及用于求解非convex结构化优化的软件。这些算法将通过保证的全局收敛来解决子问题，并在问题具有凸结构时具有最佳的计算复杂性。该算法将基于用于结构化复合最小化的近端和随机梯度方法的最新工作，用于可分离的凸/非凸优化和主动设置方法，用于多面体约束优化。此外，还将探讨用于加速融合的二阶技术。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准通过评估来获得支持的。