# Can we handle the x*y terms?

Normally, x*y is non-convex when both x and y are continuous and it makes problem intractable. However, it really appears frequently in application. If we have more constraints, like the range of one variable, i.e., 0<x<1, can we transform it into convex form? or decouple these two variables?

But there are cases where products of different variables do readily lead to convex models. For instance, consider $$\prod_{i=1}^n x_i \geq \alpha$$ with x nonnegative and \alpha\geq 0. This can be converted to an equivalent convex form $$\left(\prod_{i=1}^n x_i \right)^{1/n} \geq \alpha^{1/n}$$ The left-hand quantity is a geometric mean, which is concave and supported by CVX.