The usual good starting point is Boyd’s Convex Optimization, for a relatively rigorous but also quite practical book. The second usual, quite a bit more rigorous case is Rockafellar’s Convex Analysis, but this one deals only with general analysis as opposed to also including applications and algorithms. I highly recommend Boyd’s book, even for a mathematician ;) since it gives a lot of great motivation and is superbly written in a relatively casual yet clear style.
