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

Juan Galvez jjgalvez at um.es
Sat Nov 26 16:56:36 EST 2011

```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

```