Concave function?

(Chethan Kumar Anjinappa) #1

Hi All,

Is the function f(x,y,z) = y*log(1+(c*x/(y*z))) is concave ? If so, how can I implement it in cvx (using rel_entr)?

with x,y,z>=0

(Mark L. Stone) #2

f(x,y,z) is neither convex nor concave. For instance, at x = y = z = 1, its Hessian has 2 negative eigenvalues and 1 positive eigemvalue, so is indefinite there.

If z were a constant, not a (CVX) variable, f could be expressed as -rel_entr(y,y+c*x/z) and would be concave as a function of x and y.