Formulating the alternating current optimal power flow (ACOPF) as a
polynomial optimization problem makes it possible to solve large instances in
practice and to guarantee asymptotic convergence in theory.

用多项式优化问题表达交流最优电力流（ACOPF）问题可以在实践中解决大规模实例，并在理论上保证渐近收敛。

多项式优化问题中的最优潮流

Optimal Power Flow as a Polynomial Optimization Problem

In this paper, we provide a new framework to obtain the generalization bounds
of the learning process for domain adaptation, and then apply the derived
bounds to analyze the asymptotical convergence of the learning process. Without
loss of generality, we consider two kinds of representative domain adaptation:
one is with multiple sources and the other is combining source and target data.
In particular, we use the integral probability metric to measure the
difference between two domains. For either kind of domain adaptation, we
develop a related Hoeffding-type deviation inequality and a symmetrization
inequality to achieve the corresponding generalization bound based on the
uniform entropy number. We also generalized the classical McDiarmid's
inequality to a more general setting where independent random variables can
take values from different domains. By using this inequality, we then obtain
generalization bounds based on the Rademacher complexity. Afterwards, we
analyze the asymptotic convergence and the rate of convergence of the learning
process for such kind of domain adaptation. Meanwhile, we discuss the factors
that affect the asymptotic behavior of the learning process and the numerical
experiments support our theoretical findings as well.

本文提出了一种新的框架，通过应用获得的领域自适应学习过程的泛化界，分析了学习过程的渐近收敛。为了测量两个领域之间的差异，使用积分概率度量。通过不同的不等式和复杂度测量，证明了领域自适性学习的一些性质，并用数值实验验证了理论结果的正确性。