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


(hua meng) #1

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?


(Mark L. Stone) #2

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.


(hua meng) #3

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