A partial answer to the Demyanov-Ryabova conjecture
Optimization and Control
2017-09-07 v2
Abstract
In this work we are interested in the Demyanov--Ryabova conjecture for a finite family of polytopes. The conjecture asserts that after a finite number of iterations (successive dualizations), either a 1-cycle or a 2-cycle eventually comes up. In this work we establish a strong version of this conjecture under the assumption that the initial family contains "enough minimal polytopes" whose extreme points are "well placed".
Cite
@article{arxiv.1702.00168,
title = {A partial answer to the Demyanov-Ryabova conjecture},
author = {Aris Daniilidis and Colin Petitjean},
journal= {arXiv preprint arXiv:1702.00168},
year = {2017}
}