Cheatsheet for common convex/non-convex functions in mathematics

This is an evolving article. I’ll add more details as I get time.

The background behind this article is that when I was learning optimization (and simultaneously reading IEEE Transaction papers…what an awful time that was…hahaha :-) ), I had difficulty understanding convex vs non-convex functions. I then came to realize that I need to break down functions into their simplest forms to understand if they are convex or non-convex (the other way is to plot them and observe the graph). It was then that I made a table for myself and now I am sharing if it may be of any help to any other individual.

Feel free to correct me if I have done any mistakes or if I have missed some other common functions (which I am sure I must have). Many of the references can be directed to Stephen Boyd’s book “Convex Optimization”. Others are the process of my own toil (I did not discover them…hahaha. I just learned them through reading or watching youtube videos).

… As I said in the beginning, this is an evolving article. I am not sure how frequently I will be able to make changes to it, but I’ll do whenever and if I can.