# First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method

## TL;DR

This paper explores structure-aware presolving techniques integrated into a parallel interior-point method for large-scale linear programming, demonstrating improved performance and scalability on complex energy system models.

## Contribution

It introduces a novel implementation of presolving that preserves problem structure within a parallel interior-point framework for block-diagonal linear programs.

## Key findings

- Presolving routines significantly reduce problem size.
- Implementation achieves high performance in parallel computing environments.
- Scalability demonstrated on models with up to 700 million nonzeros.

## Abstract

In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.