How to express (x1^(-alpha/2) ) * x2^(-1)

Uncategorized
Dec 20, 2023
E
#1

There is a constraint in my program: x3 <= a1* (x1^(-alpha/2) ) * x2^(-1) , the right side has been proved to be concave when a1 is a constant and <0, alpha is a constant and > 0, x1, x2, x3 are all variables and >0 .
I tried to use pow_p(x1,-alpha/2)*pow_p(x2,-1) but CVX still cannot accept it. Is there any other way to express it?

M
#2

Hint: 4 The power cones — MOSEK Modeling Cookbook 3.3.0 and then convert to use of CVX functions.

E
#3

The problem only make sense if

x_3 \leq 0.

Given that and the other assumptions let

x_4 = x_3 / a_1 (\geq 0)

then

x_4 \geq x_1^{-\alpha/2} x_2^{-1} .

Therefore,

(x_4 x_1^{\alpha/2} x_2)^{\frac{1}{1 + \alpha/2+1}} \geq 1^{\frac{1}{1 + \alpha/2+1}}.

Sorry, I could not help myself doing it.