[Ipopt] Question regarding solving a (possibly?) non-convex model to global optimality

[Juan Galvez]

Hello,

I don't know if this is the right place to ask this (if not, please  
point me somewhere I can ask this question).

I need to solve a nonlinear programming model to global optimality  
using ipopt. I'm fairly new to this field so my knowledge is rather  
poor.

What I want to do is minimize a convex objective function subject to  
linear constraints and one constraint which I believe is non-convex.
This constraint is of the following form:

sum_{k}{a(k)*g(k)} <= C

where a(k) is a continuous variable in [0,1], g(k) is a continuous  
variable in [0,X] and C is a constant.

I can solve the problem with ipopt but I understand that to guarantee  
global optimality the problem has to be convex. I'm not sure if the  
above constraint makes the problem non-convex (and therefore ipopt  
cannot guarantee global optimality), and if so, is it possible to  
transform this constraint to equivalent convex constraints?

I'd appreciate any help.

Best regards,
Juan Galvez