Novel Decomposition Techniques Enabling Scalable Computational Frameworks for Large-Scale Nonlinear Optimization Problems

本研究计画旨在发展改良的数值最佳化演算法。该研究考虑的情况下，决策必须在缺乏完美的信息，无论是由于缺乏可靠的数据或由于不可预见的事件。大多数最先进的方法通过考虑许多潜在的场景来解决这种设置中的优化问题，这可能导致公式太大而无法直接求解。该项目的方法是根本不同的，旨在为大规模非线性连续优化创建新的分解框架。正在开发的算法将在电力系统的实际问题上进行测试。例如，分解算法将能够将大规模电网的优化分解为高压输电网的计算和与输电网相连的许多配电网相关的计算。该项目为研究生提供了研究培训机会。该项目旨在创建新的分解框架，从而产生新的实用数值算法，能够解决非线性非凸优化中某些结构化问题的显着较大的实例。这将导致计算工具的随机优化问题的解决方案时，样本平均近似产生非常大的确定性的情况下，将显着扩大阵列的易处理的随机两阶段和两级优化问题。关键的创新是一个平滑技术，克服了困境，最佳子系统的解决方案不需要可微的功能的总体系统变量。在研究的各个方面，理论将发展的特点问题重新表述和新算法的收敛保证的属性。该项目的一个预期成果是能够利用并行计算资源的高质量开源软件供公众使用。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。

This research project aims to develop improved numerical optimization algorithms. The research considers situations in which decisions must be made in the absence of perfect information, either due to the lack of reliable data or due to unforeseen events. Most state-of-the-art methods tackle optimization in this setting by considering many potential scenarios, which can result in formulations that are too large to be solved directly. The methodology in this project is fundamentally different and aims to create new decomposition frameworks for large-scale nonlinear continuous optimization. The algorithms under development will be tested on realistic questions in electrical power systems. For example, the decomposition algorithm will be able to break down the optimization of a large-scale power grid into computations for the high-voltage transmission grid and computations related to the many distribution networks that are attached to the transmission grid. This project provides research training opportunities for a graduate student.The project aims to create novel decomposition frameworks that lead to new practical numerical algorithms able to tackle significantly larger instances of certain structured problems in nonlinear nonconvex optimization than currently possible. This will result in computational tools for the solution of stochastic optimization problems when sample average approximation gives rise to very large deterministic instances and will significantly expand the array of tractable stochastic two-stage and bi-level optimization problems. The key innovation is a smoothing technique that overcomes the predicament that optimal subsystem solutions need not be differentiable functions of the overarching system variables. In all aspects of the research, theory will be developed that characterizes the properties of problem reformulations and the convergence guarantees for new algorithms. One expected outcome of this project is high-quality open-source software for public use, capable of exploiting parallel computing resources.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.