[Bonmin] nlp nonconvex problem

[Giuseppe Aprea]

Hi all,

I need to solve a NLP involving ~250 variables, lots of linear constraints and:

-a few non linear equality constraints of this form
0=h[j]=x(j0)-(( x(j1)*x(j2)*x(j3) ) / (  x(j3)+x(j4)  )),
j!=j0!=j1!=j2!=j3!=j4

in some cases there is a sum of terms similar to (( x(j1)*x(j2)*x(j3)
) / (  x(j3)+x(j4)  ))

- a non linear objective function of this form:

f=  ( (x(j1)/x(j_ref))-(C_j1/C_jref) ) * (
(x(j1)/x(j_ref))-(C_j1/C_jref) )  + similar terms with another index
j1 but the same index j_ref. C are costants

I wonder if anyone could, please, suggest

-which is the most appropiate solver between bonmin, Ipopt, couenne or lago.
-since denominators are always greater than zero but solution is
expected to have some very small components, it is worth multiplying
all nonlinear rational functions times the product of all
denominators? In this way non linearity is increased, derivatives may
become more complicated to write in the code (i.e longer and with much
more nonzero elements) but i should avoid small denominator issues if
any is present.

cheers,

giuseppe