Convexity and Optimization:

(10 points) Convexity and Optimization: (i) (2 points) Consider the function f (:12, y, z, w) = 2:2 + 311,:2 + 222 + w. Is the function convex? Detail the process that leads you to your answer. (ii) (3 points) Consider the function f (I, y, z) = 2:3 3:123;2 + 722. Is the function convex? Is the function concave? Detail the process that leads you to your answer. (iii) (2 points) State whether the following problem is convex or no. Briey explain why. min my st. 2:2 + y: g 1 m+y=1 (iv) (3 points) State whether the following problem is convex or no. Briey explain why. niax ll]2:2 5g2 + Syn: s.t. ry=1 e1+y55