http://stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

is gorgeous material. Large parts it are from theorems of the alternative, linear programming, Jensen's inequality, R. T. Rockafellar, etc., but Boyd makes it all a clean whole.

That's the upside! The downside is that, IMHO, rarely does any one person need more than a small part of the whole book, and the parts that someone needs are likely also available in the subject they are working with.

So, at least download Boyd's book and use it for reference: If ever have a question about convexity, then start with Boyd!