Question:

Let f(5t') = lls?\"2 where the norm is the Euclidean norm. Show that f satises the following relation for any 3:, y E R\" and. any oz E [0,1]: at-T + (1 - 003;) = am) + (1 - a)f(y) - 05(1 - Mll? - y\"?- 1 2 This exercise shows that the function x) 2 %||a:||2 is strongly convex with ,a = 1. Hint: the following relation may be useful 2(a, b) = \"all2 + Ill)\"2 ||a b||2, which is valid for any a, b E R\