An implementation of steepest-descent augmentation for linear programs

TL;DR

This paper presents a practical implementation of steepest-descent augmentation for linear programs, demonstrating significant computational improvements and providing insights for large-scale optimization.

Contribution

It develops a dynamic memory model for implementing steepest-descent augmentation, enabling efficient large-scale linear program solutions.

Findings

Dramatic improvements over naive approaches

Effective dynamic memory model for LP updates

Insights into large-scale linear program computations

Abstract

Generalizing the simplex method, circuit augmentation schemes for linear programs follow circuit directions through the interior of the underlying polyhedron. Steepest-descent augmentation is especially promising, but an implementation of the iterative scheme is a significant challenge. We work towards a viable implementation through a model in which a single linear program is updated dynamically to remain in memory throughout. Computational experiments exhibit dramatic improvements over a naive approach and reveal insight into the next steps required for large-scale computations.