# How to model the following problem in CVX

(Ahmed Al-baidhani) #1

I have the following optimization problem:
k_1>k_2> \ldots k_n>0, a_1>a_2> \ldots a_n>0, c_1>c_2> \ldots c_n>0, B>0, E>0 and S>0.

The term 2x_iy_i is against the DCPruleset, hence, the above problem in its current form cannot be solved with CVX. Any idea how to deal with this case?

Thanks

(Mark L. Stone) #2

That looks like a clunker to me.

Let f = 3*x^2 + 3*y^2 + 2*x*y. Hessian of f = [6 2;2 6], so f is a convex quadratic. The good news is that it can be entered in CVX as 0.5*[x y]*[6 2;2 6]*[x;y]. The bad news is that because a_i > 0, the inequality goes in the wrong direction to be convex.

(Ahmed Al-baidhani) #3