I have checked that {x^{ - a}}{y^{ - b}} is jointly convex w.r.t. x and y for x>0,y>0 (a>0 and b>0 are constant). How to transform {x^{ - a}}{y^{ - b}} into CVX form? Thanks in advance!

If in gp mode, enter it as is. Otherwise,see the first sentence of @jackfsuia 's following post if the paradigm is compatible with your usage.

I don’t believe the power cone is applicable here. And in any event, is not directly supported by CVX, so would require formulation in terms of 2nd order cones (or maybe geo_mean).

`x^(-a)y^(-b)<=z`

is equivalent to` -alog(x)-blog(y)<=log(z)`

, handle it like this. or expressing `x^(a)y^(b)z>=1`

, this can be done by using power cone per https://docs.mosek.com/modeling-cookbook/powo.html. I am not sure if Power cone is more reliable than exponential cone (the `log()`

) in general.

You need the 3 exponential cone for the log() version therefore the power cone may hold an advantage.

But you never know.

Thanks， Mark. It is very helpful.

Thanks jack. It is very helpful.

Thanks for your comments., Erling. I learn it a lot.