  Using deep neural networks to predict the solutions of AC optimal power flow
(ACOPF) problems has been an active direction of research. However, because the
ACOPF is nonconvex, it is difficult to construct a good data set that contains
mostly globally optimal solutions. To overcome the challenge that the training
data may contain suboptimal solutions, we propose a Lagrangian-based approach.
First, we use a neural network to learn the dual variables of the ACOPF
problem. Then we use a second neural network to predict solutions of the
partial Lagrangian from the predicted dual variables. Since the partial
Lagrangian has a much better optimization landscape, we use the predicted
solutions from the neural network as a warm start for the ACOPF problem. Using
standard and modified IEEE 22-bus, 39-bus, and 118-bus networks, we show that
our approach is able to obtain the globally optimal cost even when the training
data is mostly comprised of suboptimal solutions.
