Local minimum while using constraints?

[Lapin]

Hi,

I am calibrating a displaced heston model using LevenbergMarquardt method.
When I don't constraint anything the calibration works very fine.
As soon as I constraint 1 parameter to be constant (the mean reversion indeed), the calibration is much quicker (in 100 steps it is done) but the convergence is poor.

In my view it look like it finds a local minimum. The would make no real sense that there would be a behavior difference if you constraint your parameters or not but I don't find any other explanation.

Any thought?

Cheers