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arXiv · 1908.00796

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

Ambros Gleixner·Nils-Christian Kempke·Thorsten Koch·Daniel Rehfeldt·Svenja Uslu
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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.

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Ambros Gleixner, Nils-Christian Kempke, Thorsten Koch, Daniel Rehfeldt, Svenja Uslu. 2019-08-02. First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method. https://arxiv.org/abs/1908.00796

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