  We investigate how to port the standard interior-point method to new exascale
architectures for block-structured nonlinear programs with state equations.
Computationally, we decompose the interior-point algorithm into two successive
operations: the evaluation of the derivatives and the solution of the
associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both
operations using two levels of parallelism. First, we distribute the
computations on multiple processes using coarse parallelism. Second, each
process uses a SIMD/GPU accelerator locally to accelerate the operations using
fine-grained parallelism. The KKT system is reduced by eliminating the
inequalities and the state variables from the corresponding equations, to a
dense matrix encoding the sensitivities of the problem's degrees of freedom,
drastically minimizing the memory exchange. We demonstrate the method's
capability on the supercomputer Polaris, a testbed for the future exascale
Aurora system. Each node is equipped with four GPUs, a setup amenable to our
two-level approach. Our experiments on the stochastic optimal power flow
problem show that the method can achieve a 50x speed-up compared to the
state-of-the-art method.
