How to express x^(-a)y(-b) into CVX form

1

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!

2

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).

3

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.

4

You need the 3 exponential cone for the log() version therefore the power cone may hold an advantage.
But you never know.

5

Thanks， Mark. It is very helpful.

6

Thanks jack. It is very helpful.

7

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