I am trying to estimate a few unknown parameters of my continuous non-linear PDAE model (simulated through finite-volume method spatial discretisation, and time-stepping through method-of-lines). I am planning to do this by minimising the least-squares error of the model output to experimental data.
I read about the various optimisation solvers that can be used. However, I am having a weird situation. I do not have the exact analytical form of my function (since its a system of PDAES, which after discretisation yields a lot of DAEs). While, this is fairly common and the recommended method is the method of lines, I have a slightly different situation. I do have the Jacobian matrix (evaluated through Automatic Differentiation package 'CASADI').
I'd like to really take advantage of the power of the jacobian matrix, i.e. directional information towards solution. Furthermore, my function evaluation is very cheap, since my simulation model is hand-optimised and takes advantage of various intrinsic CPU instructions.
What would be the recommended software package for implementing a global optimisation for parameter estimation, given this situation ?