How to express 1/(y *(1-x)) in CVX, and y>0; 0<x<1 are the constraints.

I calculated the Hessian matric

Assume you need

t \geq \frac{1}{x*z},\quad x,z\geq 0.

Therefore,

(t*x*z)^{1/3} \geq 1

implying the geometric mean of (t,x,z) must be greater than one.

As far as I remember there is geo_mean function in cvx.

Yes, `geo_mean([t,y,1-x]) >= 1`

can be used Then use `t`

in place of `1/(y*(1-x))`

.

Alternatively, `prod_inv([y,1-x])`

can be directly used in place of `1/(y*(1-x))`

. CVX converts this under the hood to the `geo_mean`

formulation.