# Parallel Interior-Point Solver for Block-Structured Nonlinear Programs on SIMD/GPU Architectures

arXiv: https://arxiv.org/abs/2301.04869 · HTML: https://mlsanity.com/paper/2301.04869/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Application of deep and reinforcement learning to boundary control problems](https://mlsanity.com/paper/2310.15191/) (2023)

## Abstract (arXiv)

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.