# Solving Linear Programming While Tackling Number Representation Issues

### Adrien Chan-Hon-Tong

#### 2022

#### Abstract

Gaussian elimination is known to be exponential when done naively. Indeed, theoretically, it is required to take care of the intermediary numbers encountered during an algorithm, in particular of their binary sizes. However, this point is weakly tackled for linear programming in state of the art. Thus, this paper introduces a new polynomial times algorithm for linear programming focusing on this point: this algorithm offers an explicit strategy to deal with all number representation issues. One key feature which makes this Newton based algorithm more compliant with binary considerations is that the optimization is performed in the so-called first phase of Newton descent and not in the so-called second phase like in the state of the art.

Download#### Paper Citation

#### in Harvard Style

Chan-Hon-Tong A. (2022). **Solving Linear Programming While Tackling Number Representation Issues**. In *Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-548-7, pages 40-47. DOI: 10.5220/0010812300003117

#### in Bibtex Style

@conference{icores22,

author={Adrien Chan-Hon-Tong},

title={Solving Linear Programming While Tackling Number Representation Issues},

booktitle={Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2022},

pages={40-47},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010812300003117},

isbn={978-989-758-548-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Solving Linear Programming While Tackling Number Representation Issues

SN - 978-989-758-548-7

AU - Chan-Hon-Tong A.

PY - 2022

SP - 40

EP - 47

DO - 10.5220/0010812300003117