Revisiting simplex method in the light of Chubanov algorithm.

Adrien Chan-Hon-Tong (1)

1 DTIS, ONERA, Université Paris Saclay (COmUE) [Palaiseau]

Simplex core is to move from vertices to vertices following edges. This short paper argues that it could be relevant to modify simplex with a specific preprocessing, and, the strongly polynomial time Chubanov algorithm for homogeneous linear feasibility. The preprocessing links moving far away from constraints and minimizing the objective value. This way, one could move from vertices to vertices following faces of undertermined dimension. Then, Chubanov algorithm can be used to solve the homogeneous linear feasibility problem corresponding to the computation of such move. The main feature of this algorithm is to handle both singular and non singular vertices in a strongly polynomial number of operations contrary to raw simplex method which may takes exponential time to exit a degenerated vertex. Despite, there is little hope that complexity is strongly polynomial in worse case (as core of the algorithm is close to simplex core), the offered algorithm may outperforms interior point state of the art if binary size is very large compared to number of vertices, and, marginally, opens the question about if moving along faces may lead to a faster convergence than moving along edges.

Mots clés: Strongly polynomial; Linear programming

Domaines: Recherche opérationnelle [math.OC]

Adrien Chan-Hon-Tong. Revisiting simplex method in the light of Chubanov algorithm.. 2019. ⟨hal-00722920v18⟩