[pz]

convex optimization covers a lot of different problem types. in general, you are trying to minimize (or maximize) some function (the objective function) over a set of variables subject to a set of constraints on those variables. 'convex optimization' deals specifically with optimization problems where the objective function is... convex. this essentially means you can efficiently find the global minimum (or maximum if the function is concave)

ok, so a simple example: lets say you're on a hacker's budget and you want to maximize your caloric intake given your limited funds. This is your objective function. BUT, if you're like me, you can't live on ramen and mountain dew... i have a basic set of nutritional requirements. These are your constraints. For example, sodium has to be less than A and protein greater than B and so on and so forth. So you are essentially optimizing over ALL possible diets.

My guess is you'd end getting back: kale, potatoes and beans. Now that's a real hacker's diet!