Linearization of a non linear contraint (min between two positive variables)

Question

I have the following restriction: min(A, B), where A and B are always positive. It's very simple to linearize this using binaries, but I have a NLP problem and I don't know how to approach this.

I have tried some approximations as max(-A,0) = (-A + sqrt(-A^2 + error^2)/2 but they don't really apply to my problem.