论文标题
通过BI级SQP和ADMM分散的非凸优化
Decentralized non-convex optimization via bi-level SQP and ADMM
论文作者
论文摘要
在许多实际相关性问题中，分散的非凸优化非常重要。但是，现有的分散方法通常缺乏对一般非凸问题的融合保证，或者它们的子问题复杂性很高。我们提出了一种新型的双层SQP方法，其中通过ADMM解决了内部二次问题。牛顿方法的分散式停止标准可以提前终止ADMM作为内部算法，以提高计算效率。该方法具有针对非凸问题的局部收敛保证。此外，它仅求解二次程序的序列，而许多现有算法求解了非线性程序的序列。该方法显示出最佳功率流问题的竞争性数值性能。
Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.
