[benrbray]

I'm not sure "Convex Optimization" by B&V is a good self-study book. I really struggled with it as student, and I struggled to teach with it as a TA.

It's one of those "Step 2. Draw the Rest of the Owl!" books. Great as a reference manual, but not great pedagogically. It's very complete and I would struggle to name anything better, though. Mostly, I learned convex analysis by scouring Google for lecture notes written by random professors, then cross-referencing with B&V.

[wheelinsupial]

How is the notation and standards in convex optimization?

I took a course linear programming out of Vanderbei's book and it seemed any time I used google to find notes that everyone used slightly different notation or methods. For example, Vanderbei used the dictionaries and others used the tableau.

[benrbray]

It's quite a mess, since discrete optimization is quite an old topic used by many different fields (engineering, statistics, sciences, math) each with their own notation/terminology. One of the merits of the B&V book is the relatively clear/precise notation, and they've made an effort to disambiguate. That's why it's so well-regarded as reference material.