Reviews: Accelerating Rescaled Gradient Descent: Fast Optimization of Smooth Functions

I think the first part of the paper has very good original contributions with correct and nicely-written proofs in the appendix. However, I have the following questions regarding the parts of the paper starting at Section 3. Sorry if these are redundant questions with obvious answers that I missed. The RGD framework is mentioned for both convex and non-convex functions (Lemma 4 doesn't require f to be convex). However, the examples provided are all convex functions, and the focus also seems to be quite heavily on convex functions (because none of the papers on nonconvex optimization are compared with). Do the authors have (1) theoretical results and comparisons with existing work and/or (2)experiments, for non-convex functions?