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

1

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

2

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.

3

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.

5

Thank you for your answering.
I tried prod_inv([y,1-x]), I wonder whether this is inv_prod(), after I had changed this, it has an error ValueError: The input must be a single CVXPY Expression, not a list. Combine Expressions using atoms such as bmat, hstack, and vstack. And I delet “” as inv_prod(y,1-x), it has an another error TypeError: inv_prod() takes 1 positional argument but 2 were given. So I wonder how to solve it? Thanks!

6

Thank you for your answering! I will try this method!

7

This is the CVX forum, for CVX, which runs under MATLAB. prod_inv is a CVX function.

inv_prod is the corresponding function for CVXPY. If you need help with that, see FAQ — CVXPY 1.5 documentation .

8

Thanks a lot! I get it!