And here you want to know about the operations that preserve convexity, and we look at sort of the really obvious simple ones, you know, nonnegative weighted sum, that’s kind of obvious. Composition if an affine function, that’s also very easy to show. Pointwise maximum supremum, we looked at examples too, and by the time you get to sort of supremum, you can actually start showing convexity of some things that at first glance look pretty complicated. ...

See the whole transcript at Convex Optimization I - Lecture 04