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The existence of a strongly polynomial time simplex method
release_u7rbemhmbjakzbnlk6iqbe2ouy
by
Zi-zong Yan, Xiang-jun Li, Jinhai Guo
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2021
Abstract
It is well known how to clarify whether there is a polynomial time simplex
algorithm for linear programming (LP) is the most challenging open problem in
optimization and discrete geometry. This paper gives a affirmative answer to
this open question by the use of the parametric analysis technique that we
recently proposed. We show that there is a simplex algorithm whose number of
pivoting steps does not exceed the number of variables of a LP problem.
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arXiv
2006.11466v7
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