How to convert sqrt( 1-(1+x/y)^(-2) ) to a formula that can be expressed in CVX?

Nonconvex
1

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.

2

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

3

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

4

Thanks for your answer. But I’m soory I didn’t describe my problem completely. In fact, I want to express log(1+γ) -asqrt(V) in CVX(I want to maximize it), where x, y are variables, γ=bx/(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.

5

Thanks for your answer. I will read it carefully.

6

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.