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.

翻译：大规模基础设施网络的运行需要可扩展的优化方案。为确保系统安全运行，在少量迭代次数内实现高可行性至关重要。分解方案有助于实现可扩展性。然而，在可行性方面，传统方法如交替方向乘子法（ADMM）通常收敛缓慢。本文针对具有层次结构的强凸二次规划问题提出了原始分解方案。这些方案在少量迭代次数内即可提供高可行性，同时具备全局收敛性保证。我们在决策变量和约束数量高达300,000的问题上，将所提方案与集中式现成内点求解器Ipopt以及ADMM进行性能对比。研究发现，所提方法能以与Ipopt相当的速度求解问题，同时减少通信需求且无需完整模型交换。此外，所提方案相比ADMM能达到更高的求解精度。