x^4/y^2 +y^4/x^2+2xy : this is giving me a lot of problems. I believe I can use quad_over lin to solve this, but am unsure. Of course, I believe that there’s some factorization going on here. I do know it is convex. Any pointers appreciated here.
x^4/y^2 + y^4/x^2 + 2*x*y is convex, but I haven’t proven it. Please show us your proof. bonus points if its constructive using CVX (DCP) building blocks. if your proof is constructive, that can be a guide for the CVX formulation.
If it is convex, it may take another poster more clever than me to provide a CVX reformulation.
x^4/y^2 +y^4/x^2+2xy = (x^2/y+y^2/x)^2. It’s a composition of quad_over_lin and g(u,v)=(u+v)^2 , which is convex and non-decreasing. Therefore if x,y>0, this problem can be solved by minimizing
pow_pos(quad_over_lin(x, y) + quad_over_lin(y, x), 2). Note that
pow_pos(,2) instead of
power(,2) should be used here.
@Gengchen-Wei Very nice.
In this case it is a little simpler to use
square_pos(...) instead of