How to express this normalized square objective function?

(Dipak Narayanan) #1

Let \bf d is a vector of size 1\times N
\bf s is also a vector of size 1\times N

Now, the objective I have is

\text{minimize }\max\hspace{1mm} \left(\frac{d_i-s_i}{d_i}\right)^2

Is there a way to express it in CVX?

(Mark L. Stone) #2

Have you proven it is convex, as is your responsibility? Why isn't CVX accepting my model? READ THIS FIRST!

According to my calculations, the Hessian of ((d - s)/s)^2 evaluated at d = 2, s = 1 has one positive and one negative eigenvalue, so not convex. Actually, I think it is indefinite (neither convex nor concave) everywhere except for d = s.