Hello everyone,
I need help in solving some questions for convex functions.
We know that the addition of convex functions f+g is convex. But, I want to check whether that is the case for subtraction and f(g(x). I already solved but I am doubting my ways, plus subtraction shows that it does imply convex but not sure if that is true.
#Convex Functions
flat lava
lament sunBOT
flat lava
Not sure what this goeds under, I put algebra since it could be proved algebraically.
analog laurel
Substraction can be convex or concave or none
flat lava
So addition always results in convex and subtration doesnt, what about the rest?
flat lava
it is not true
I know of examples which is why I was confused at my result. I basically had the inequality f(tx + (1 − t)y) - g(tx + (1 − t)y) ≤ tf(x) + (1 − t)f(y) -((tg(x) + (1 − t)g(y))
LHS becomes h(x) since h(x) = f-g
RHS can be simplified to:
(1-t)(f(x)-g(x)+t(f(y)-g(y))
flat lava
Substraction can be convex or concave or none
Yes I believe so too but not sure what I did wrong with my inequality.
analog laurel
I know of examples which is why I was confused at my result. I basically had the...
If h(x) = f(x)-g(x) then LHS is h(tx+(1-t)y) and RHS is th(x) + (1-t)h(y)
Idk how did you get those results
flat lava
I expanded it.
I had h(x) on LHS be h(t(x+(1-t)y) which is the same thing.
I think I tried to work backwards.
flat lava
how do i solve this?