Convex functions A functionf:R>R is convex if for all a,B≥0 such that a+β=1, we have fax+阝y)≤o(x)+B/f orax,y∈ R f afx)+ B) f fax+阝y) x ax+ B c 2001 by Charles E Leiserson Introduction to Agorithms Day 17 L9.7© 2001 by Charles E. Leiserson Introduction to Algorithms Day 17 L9.7 Convex functions A function f : R → R is convex if for all α,β ≥ 0 such that α + β = 1, we have f(αx + βy) ≤ αf(x) + βf(y) for all x,y ∈ R. αx + βy αf(x) + βf(y) f(αx + βy) x y f(x) f(y) f