Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

Terlaky, Tamás

doi:10.1007/s11750-013-0293-9

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2020

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“…The Hirsch conjecture, closely related to this open question, has received a lot of attention due to Santos' recent counter-example [24]. On the subject for more information see the papers [3,7,18,19] and the comments [5,10,15,25,29].…”

Section: Introductionmentioning

confidence: 99%

The existence of a strongly polynomial time simplex algorithm for linear programming problems

Yan¹,

Li²,

Guo³

2020

Preprint

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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. Under the assumption of regularization, this paper gives a affirmative answer to this open question by the use of the parametric analysis technique. We show that there is a simplex method whose number of pivoting steps does not exceed the number of variables of a LP problem.

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