Homework 1

Homework 1 Ana Huaman March 9, 2011 1. In class it was claimed that given a function h : 0 (from the definition of directional derivatives). So, we can eliminate it safely: dT ∇L(u∗ )α > 0

(11)

is a condition for L(u∗ ) to be a minimum, considering directional derivatives. So, the FONC for this case is given by Eq. 11, namely: dT ∇L(u∗ ) ≥ 0 6. Let L ∈ C 1 be convex, i.e., L(αu1 + (1 − α)u2 ) ≤ αL(u1 ) + (1 − α)L(u2 ), ∀u1 , u2 ∈