[Ipopt] question on formulation of the objective function and IPOPT performance

[Damien]

All,

I'm looking at two ways to formulate the objective function in a new 
optimisation model.  The first way is what you'd call the conventional 
way I suppose, where you have a variety of variables contributing to the 
objective value and you calculate the gradient and return that to 
IPOPT.  The other way I'm considering is to equate the objective 
function to a new variable in an extra equality constraint, and have the 
new variable as the only variable in the objective, with a gradient of 
1.0.  The new equality constraint then contributes first partial 
derivatives like any other equation or constraint.

Mathematically (and I think algorithmically) these are equivalent, but I 
was wondering if anyone who's done this before has seen a performance 
difference between the two.

Cheers,

Damien