The existence of a strongly polynomial time simplex algorithm for linear programs
Optimization and Control
2022-10-03 v9
Abstract
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by using the parameter analysis technique presented by us (arXiv:2006.08104). We show that there is a simplex algorithm whose number of pivoting steps does not exceed the number of variables of a LP problem.
Cite
@article{arxiv.2006.11466,
title = {The existence of a strongly polynomial time simplex algorithm for linear programs},
author = {Zi-zong Yan and Xiang-jun Li and Jinhai Guo},
journal= {arXiv preprint arXiv:2006.11466},
year = {2022}
}
Comments
16 pages, 0 figure