Basically because if f is concave, then -f is convex. So say we have: f(x) <= g(x) with f convex, and g concave. then that means ... <看更多>

Hint. Try f(x)=ex (convex) and g(x)=−x2 (concave). What about f(g(x))=e−x2? Is it convex or concave? P. S. If we assume that f,g are C2 then ... ... <看更多>

2 Concave Functions. Definition 4. On a convex set A ⇢ RN, a function f : A ! R is concave (convex) if 8x,x0 2 A and a 2 (0,1],. ... <看更多>