This short discussion paper comments on Francisco Santos’ excellent review paper Recent Progress on the Combinatorial Diameter of Polytopes and Simplicial Complexes. We provide some notes on a few closely related topics that were not covered in the survey paper, such as: some relaxed version...

Recently, using the framework of self-regularity, Salahi in his Ph.D. thesis proposed an adaptive single step algorithm which takes advantage of the current iterate information to find an appropriate barrier parameter rather than using a fixed fraction of the current duality gap. However, his...