CAREER: Structure-Exploiting Optimization for Power Systems and Applications to Large-Scale Networks

职业：电力系统的结构利用优化和大规模网络的应用

• 批准号: 2047462
• 负责人: Richard Zhang
• 金额: $ 50万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-02-01 至 2026-01-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2047462&HistoricalAwards=false
• 关键词: CAREER; Structure; Exploiting; Optimization; Power

This NSF CAREER project will investigate structure-exploiting optimization techniques for power system optimization. The project seeks radical, transformative improvements upon the state-of-the-art by identifying and exploiting the mathematical structures that make power system optimization fundamentally distinct from general purpose optimization. While power system optimization is intractable in the worst case, the advantage of a structure-specific technique is that it can preferentially target those more tractable instances that appear in the real world. The intellectual merits of the project include: (i) provable guarantees on a high-quality solution within a fixed amount of computing time; via (ii) low-complexity algorithms that directly and explicitly make use of tree-like graph property of electric grids; and (iii) understanding and exploiting the convex-like behavior in the quadratic nonlinearity between voltage and power. The broader impacts of the project include: (i) addressing the urgent need for software capable of meeting the safety-critical, large-scale, and time-sensitive needs of power systems; (ii) technology transfer to other societal applications with a large-scale network structure, such as transportation, network statistics, machine learning, and artificial intelligence; and (iii) integration of research and education at the University of Illinois, including outreach efforts to attract and inspire K-12 students and educators. What makes power system optimization particularly challenging is that it entails making safety-critical decisions on a large-scale system over a short span of time. General-purpose optimization techniques are often too broad and all-encompassing to meet the specific needs of the system. In developing structure-exploiting techniques, this project will focus on two mathematical structures that have shown exceptional promise in the existing and related literature. The first is the tree-like graph structure of the electric grid, which allows many of the hardest combinatorial optimization to be easily solved. Our study will aim to resolve whether power system optimization can be easily solved on a tree-like graph. The second is the quadratic nonlinearity between power and voltage, which exhibits a convex-like behavior despite not being convex. The project will seek to guarantee this convex-like behavior, and to explore its implications for large-scale 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.

这个NSF的职业生涯项目将调查结构开发优化技术的电力系统优化。该项目通过识别和利用使电力系统优化从根本上区别于通用优化的数学结构，寻求对最先进技术的根本性、变革性改进。虽然电力系统优化在最坏的情况下是棘手的，但特定于结构的技术的优点是它可以优先针对那些出现在真实的世界中的更易处理的实例。该项目的智力优势包括：（i）在固定的计算时间内对高质量解决方案的可证明保证;（ii）直接和明确利用电网的树状图形属性的低复杂性算法;以及（iii）理解和利用电压和功率之间的二次非线性中的凸状行为。 该项目的更广泛影响包括：（i）解决对能够满足电力系统安全关键，大规模和时间敏感需求的软件的迫切需求;（ii）向具有大规模网络结构的其他社会应用程序进行技术转让，如运输，网络统计，机器学习和人工智能。以及（iii）伊利诺伊大学的研究和教育一体化，包括吸引和激励K-12学生和教育工作者的外展工作。使电力系统优化特别具有挑战性的是，它需要在短时间内对大规模系统做出安全关键决策。通用优化技术通常过于宽泛和包罗万象，无法满足系统的特定需求。在开发结构开发技术，这个项目将集中在两个数学结构，已显示出特殊的承诺，在现有的和相关的文献。首先是电网的树状图结构，它允许许多最困难的组合优化很容易解决。我们的研究将旨在解决电力系统优化是否可以很容易地解决一个树状图。第二个是功率和电压之间的二次非线性，尽管不是凸的，但它表现出类似凸的行为。该项目将寻求保证这种凸状行为，并探索其对大规模优化的影响。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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

Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations

• 发表时间: 2022-11
• 作者: Hong-Ming Chiu;Richard Y. Zhang

Preconditioned Gradient Descent for Over-Parameterized Nonconvex Matrix Factorization

• 发表时间: 2021
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Jialun Zhang;S. Fattahi;Richard Y. Zhang

Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion

• DOI: 10.48550/arxiv.2208.11246
• 发表时间: 2022-08
• 期刊: ArXiv
• 作者: G. Zhang;Hong-Ming Chiu;Richard Y. Zhang

Preconditioned Gradient Descent for Overparameterized Nonconvex Burer-Monteiro Factorization with Global Optimality Certification

• DOI: 10.48550/arxiv.2206.03345
• 发表时间: 2022-06
• 期刊: ArXiv
• 作者: G. Zhang;S. Fattahi;Richard Y. Zhang