How to express this kind of constraint (cube over linear) in cvx?

hi, dear everyone.
i want express x^3/y and x^2/y (x>0,y>0) in cvx as constraints. i’ve used hessian to proof that it’s convex. but when i run the program, the window say "Cannot perform the operation: {convex} .* {convex} ". how can i express them in another way? or how can i solve this problem?
here is my expression, pai and vm[n] are variables.

i solved this problem with relaxation variable, in this web, i saw this function quad_over_lin, so x^2/y can easily reformulate it to quad_over_lin(x,y), then for x^3/y, we can add one relaxation variable x_t >= pow_abs(x,(3/2)), then reformulate it to quad_over_lin(x_t,y).

In a similar manner, x^3/y^2 for x,y >= 0 can be modeled per @Michal_Adamaszek’s formulation How can I write this kind of constraint (cube over square) in cvx

Another place to find quad_over_lin, and many other CVX functions, is the CVX Users’ Guide.

New functions for CVX


Overloading for CVX of existing MATLAB functions

I recommend you read it in order to get maximum benefit from CVX (we are all optimizers here, are we not?). Along with reading and searching this forum.

Note: I edited the thread title to make it easier to search for. I also edited the title of the thread containing @Michal_Adamaszek’s solution to include “cube over square”.

thank you, dear mark, i’ll check and try to adjust my code again!