Invalid quadratic form(s): not a square problem

Nonconvex
1

Hi,

I am trying to insert function f=1/(xy) as my constraint in a optimization problem, where (x>0) and (y>0) are optimization variables. The hessian can be written as g=3/(x^4*y^4)>0 which is a convex function. How can i write it in the cvx properly?

Thanks.

2

g is not the Hessian.

f == 1/(x*y) is a nonlinear inequality constraint, and is non-convex.

1/f <= x*y (with x >= 0, y >= 0) is a rotated second order cone, and can be handled using rotated_lorentz as
{sqrt(1/f),x,y} == rotated_lorentz(1)

3

Thank you so much for your prompt reply.
My constraint is 1/(x*y)>=Constant, so i think rotated_lorentz can not be used. Hence, I decided to apply first-order Taylor expansion for LHS of this constraint.