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

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。随着技术的进步，海量、噪声和非结构化数据几乎存在于现代科学研究的方方面面。通过更复杂的优化模型有效地利用大数据以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标准，而优化模型中最具挑战性的非凸性和不可微性被抛弃和忽略。后者性质在现代科学和工程应用中的普遍存在要求新的理论和计算算法。两阶段随机规划是一种最优化模型，其中部分决策必须在观测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。该奖项致力于为大规模非凸非光滑两阶段随机规划设计计算框架，这些规划在理论上是严格的，在数值上也是有效的。该方法的关键是一种新的提升技术，它揭示了复值函数的隐含凸凹结构。研究人员的目标是(I)设计分解方案并分析其收敛；以及(Ii)研究采样技术和分解算法的融合以加速收敛。该奖项反映了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。

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.