Let be a Compact Convex Set. Let be a Continuous Convex Function. Then achieves its maximum at an Extreme Point of . Proof Let . It exists as is Compact and is Continuous Now set As is Continuous, is open (in ) As is a Convex Function, is a Convex Set. Suppose contains all Extreme Points of TODO Somewhere here, there is a proof that , but I can’t find it rn.