  This paper introduces a framework to capture previously intractable
optimization constraints and transform them to a mixed-integer linear program,
through the use of neural networks. We encode the feasible space of
optimization problems characterized by both tractable and intractable
constraints, e.g. differential equations, to a neural network. Leveraging an
exact mixed-integer reformulation of neural networks, we solve mixed-integer
linear programs that accurately approximate solutions to the originally
intractable non-linear optimization problem. We apply our methods to the AC
optimal power flow problem (AC-OPF), where directly including dynamic security
constraints renders the AC-OPF intractable. Our proposed approach has the
potential to be significantly more scalable than traditional approaches. We
demonstrate our approach for power system operation considering N-1 security
and small-signal stability, showing how it can efficiently obtain cost-optimal
solutions which at the same time satisfy both static and dynamic security
constraints.
