大规模基础设施网络的可扩展原始分解方案
Scalable Primal Decomposition Schemes for Large-Scale Infrastructure Networks
AI总结：
针对大规模基础设施网络运行需可扩展优化方案的需求，提出分层结构强凸二次规划的原始分解方案，其在少量迭代中具高度可行性且全局收敛，基准测试显示求解速度与Ipopt相当、通信量更少且准确性高于ADMM。
摘要：
大规模基础设施网络的运行需要可扩展的优化方案。为保证系统安全运行，在少量迭代中实现高度可行性至关重要。分解方案有助于实现可扩展性，但在可行性方面，交替方向乘子法（ADMM）等经典方法往往收敛缓慢。本研究针对分层结构强凸二次规划（QPs）提出原始分解方案，这些方案结合全局收敛保证，能在少量迭代中实现高度可行性。我们在含至多300,000个决策变量和约束的问题上，将其性能与集中式现成内点求解器Ipopt及ADMM进行基准测试，发现所提方法求解速度与Ipopt相当，但通信量减少且无需完整模型交换，同时准确性高于ADMM。
英文摘要：
The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to achieve scalability. In terms of feasibility, however, classical approaches such as the alternating direction method of multipliers (ADMM) often converge slowly. In this work, we present primal decomposition schemes for hierarchically structured strongly convex QPs. These schemes offer high degrees of feasibility in a small number of iterations in combination with global convergence guarantees. We benchmark their performance against the centralized off-the-shelf interior-point solver Ipopt and ADMM on problems with up to 300,000 decision variables and constraints. We find that the proposed approaches solve problems as fast as Ipopt, but with reduced communication and without requiring a full model exchange. Moreover, the proposed schemes achieve a higher accuracy than ADMM.
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