# a list of known convex functions?

I am working on the development of novel optimization algorithm where it DOES NOT suffer from the non-differentiability (cf. subgradient), which also works well in differentiable class of the objectives.

Now, I want to explore the behaviour of my algorithm. I only took relavant optimization courses like 4 lectures, but it does not necessarily mean I am super good or much experienced in this field.

So, is there any good article which $\mathbf{LISTS}$ interesting known convex objectives at a single sight for this purpose? Or should I manually try this and that based on my own experience so far?

• You can search for "review article". Those are articles broadly speaking trying to summarize the current state of a topic. Well, if it is new anyway. – mathreadler May 7 '18 at 7:00
• The search term you need is benchmark problems. – Rahul May 7 '18 at 7:21
• Such a method already exists. See optimization-online.org/DB_HTML/2013/04/3833.html. Also, a convex function on an open set is twice differentiable almost everywhere, so there is no practical difference between differentiability and subdifferentiability for convex problems. – Serg May 7 '18 at 7:38
• @Serg , "There is no practical difference between differentiability and subdifferentiability for convex problems". It is hard to say so. I shortly checked your reference, clearly it is sublinear, which is a typical story. My goal is to achieve even superlinear. – Robin May 8 '18 at 7:42
• @Robin. The method i linked to is optimal. This is as good as it gets without additional assumptions like strong convexity. Even linear global convergence is impossible to achieve for non strongl convex objectives. – Serg May 8 '18 at 7:54