hello everyone! I met a problem about how to convert sqrt( 1-(1+x/y)^(-2) ) to a formula that can be expressed in CVX? where x and y are variables greater than 0. You can use auxiliary variables for processing, but I can’t solve it. If you can solve this problem, please reply to me. Thank you for your answer, please help me.

For x=1 the expression as a function of y is neither convex nor concave.

Following up on @Michal_Adamaszek post, @c_stone please carefully read Why isn't CVX accepting my model? READ THIS FIRST!

Thanks for your answer. But I’m soory I didn’t describe my problem completely. In fact, I want to express log(1+γ) -a*sqrt(V) in CVX(I want to maximize it), where x, y are variables, γ=b*x/(c*y+d) , V=1-(1+γ)^(-2) and a,b,c,d are constants. x and y meet the following restrictions:0<x<1, 0<y<1. I can handle the first part of the formula, but I can’t deal with the second part of the formula.

Thanks for your answer. I will read it carefully.

By first part of the formula, do you mean `log(1+b*x/(c*y+d))`

? If so, how are you handling that? The special case `log(1+x/y)`

is neither convex nor concave at various points in `0 < x < 1. 0 < y < 1`

; and therefore can’t be represented in CVX.