Solving Linear Programming While Tackling Number Representation Issues

Adrien Chan-Hon-Tong

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Paper

Solving Linear Programming While Tackling Number Representation Issues

Topics: Linear Programming; Optimization

In Proceedings of the 11th International Conference on Operations Research and Enterprise Systems ICORES - Volume 1, 40-47, 2022

Author: Adrien Chan-Hon-Tong

Affiliation: ONERA, Université Paris Saclay, France

Keyword(s): Linear Programming, Polynomial Time Complexity, Number Representation.

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.

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Paper citation in several formats:

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 - ICORES; ISBN 978-989-758-548-7; ISSN 2184-4372, SciTePress, pages 40-47. DOI: 10.5220/0010812300003117

@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 - ICORES},
year={2022},
pages={40-47},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010812300003117},
isbn={978-989-758-548-7},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of the 11th International Conference on Operations Research and Enterprise Systems - ICORES
TI - Solving Linear Programming While Tackling Number Representation Issues
SN - 978-989-758-548-7
IS - 2184-4372
AU - Chan-Hon-Tong, A.
PY - 2022
SP - 40
EP - 47
DO - 10.5220/0010812300003117
PB - SciTePress