how to model a non-convex function in its convex area

[bao hanqiu]

Dear Johan,

 I have a problem which i cannot handle.

For example,  sqrt((1 - t)/t) is convex as  0<t≤0.75. So how can I model sqrt((1 - t)/t)<=2 ,  0<t≤0.75 in yalmip to make yalmip recognize this constraint as a convex constraint?

Thanks  a lot!

Hanqiu Bao

[Johan Löfberg]

Why would you complicate it? t>=0.2 and you are done.

[bao hanqiu]

Because what I need to solve is a complex constraint, for instance, ax+sqrt((1-t)/t)<=b, where both x and t are optimization variables

[Johan Löfberg]

I don't see any easy way. If possible, it will require a series of clever variable changes and sandwiching.

[Michal Adamaszek]

Suspected to be not possible to represent exactly with standard cones:

https://ask.cvxr.com/t/how-to-program-sqrt-1-x-x/7040

[bao hanqiu]

Thanks a lot!