Is x/log(1+x) concave? How can I use cvx solve the constraints " x/log(1+x) >= C", where C is constant

Nonconvex
Apr 2, 2022
K

Is x/log(1+x) concave? If yes? How can I use cvx solve the constraints " x/log(1+x) >= C", where C is constant.

M

Presuming x >= 0, that would be x >= log(1+x)*C, which is a non-convex constraint if C > 0, and is a convex constraint if C < 0.

You should be coming to us with a convex constraint, which you have proven to be convex, not asking us whether it is convex.

J

Yes, when x>0, it’s cocave. Expressing it is equivalent to Expressing the following

K
Replying to #2

Received with thanks.

K
Replying to #3

WoW! That is a great idea. Thank you~