The function `-xlog(1+y)` for variables x>0 and variable y>0, could be directly used in CVX?

Nonconvex
Oct 8, 2017
R

Hi,
The function -xlog(1+y) for scale variable x>0 and scale variable y>0, could be directly used in CVX? More generally, it can be available for vector x and y used in CVX?

M

The determinant of its Hessian is -(1+y)^(-2), therefore it must have one positive eigenvalue and one negative eigenvalue. So the function is indefinite, i.e., neither convex nor concave, and it can not be used in CVX.

R
Replying to #2

That’s right, thank you for your help, Mark!