CRII: CCF: AF: Decomposition Algorithms for nonconvex nonsmooth constrained stochastic programs

CRII：CCF：AF：非凸非光滑约束随机程序的分解算法

• 批准号: 2416172
• 负责人: Ying Cui
• 金额: $ 17.49万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2416172&HistoricalAwards=false
• 关键词: CRII; CCF; AF; Decomposition; Algorithms

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).With the advance of technology, massive, noisy and unstructured data are prevalent in almost every aspect of modern scientific research. It is crucially important to harness big data effectively via more complicated optimization models to make reliable decisions. The handy properties of convexity and smoothness have become the norm of the field traditionally, and the most challenging features of the optimization models, nonconvexity and nondifferentiability, are abandoned and ignored. The pervasiveness of latter properties in the modern science and engineering applications calls for new theory and computational algorithms. Two-stage stochastic programs are optimization models where partial decisions have to be made before the observation of any uncertain parameter, while the remaining decisions are determined after the full information is revealed. This award focuses on designing computational frameworks for large-scale nonconvex and nonsmooth two-stage stochastic programs that are both theoretically rigorous and numerically efficient. The crux of the approach is a novel lifting technique that exposes an implicitly convex-concave structure of the complex value function. The investigator aims to (i) design decomposition schemes and analyze their convergence; and (ii) investigate a fusion of the sampling technique and the decomposition algorithms to accelerate the convergence.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.

该奖项全部或部分由《2021年美国救援计划法案》（Public Law 117-2）资助。随着技术的进步，海量、嘈杂和非结构化的数据几乎普遍存在于现代科学研究的各个方面。通过更复杂的优化模型有效地利用大数据来做出可靠的决策至关重要。传统上，凸性和光滑性等方便的性质已经成为该领域的规范，而优化模型最具挑战性的特征，非凸性和不可微性，则被抛弃和忽视。后一种性质在现代科学和工程应用中的普遍性要求新的理论和计算算法。两阶段随机规划是一种优化模型，其中部分决策必须在观察到任何不确定参数之前做出，而其余决策则在全部信息被揭示之后确定。该奖项的重点是设计大规模非凸和非光滑两阶段随机程序的计算框架，这些程序在理论上是严格的，在数值上是有效的。该方法的关键是一种新的提升技术，揭示了一个隐式的凹凸结构的复值函数。该奖项旨在（i）设计分解方案并分析其收敛性;（ii）研究采样技术和分解算法的融合，以加速收敛性。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

A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse Functions

具有非凸追索函数的两阶段随机规划的分解算法

• 发表时间: 2024
• 期刊: SIAM Journal on Optimization
• 影响因子: 3.1
• 作者: Hanyang Li;Ying Cui
• 通讯作者: Ying Cui

On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models

• 发表时间: 2022-08
• 作者: Yangjing Zhang;Ying Cui;B. Sen;K. Toh