I don’t understand the notation. For example, what are A_m(X), B_m(x) ? Doesn’t each term in the objective simplify to \frac{A_m(x)}{B_m(x)}?
Anyhow, the first thing is, how did you prove convexity, i.e., that the objective function is concave? What do you know about the sign of B_m(x)? (I guess you are trying to constrain it to be >= 0 and <= 1)?