Gradient-based minimization and gradients

[LisaSchlueter]

The default algorithm of the Optim minimizer is Nelder-Mead(), which is a gradient-free method. I'd like to explore gradient-based algorithms, such as GradientDescent() or LBFGS(). Motivation:

• We sometimes get weird fit results of calibration gamma peaks
• When testing combined fits or comparing the different peakshape-models, the fit sometimes unreliable (local minimum?)
• Choice of some pseudo-prior (e.g. skew fraction) have unrealistic strong impact on fit result

When going to a gradient-based algorithm, it would make sense to provide the minimizer with the analytical gradients. @oschulz do you have experience on how to do that in julia?

[oschulz]

In principle we can used automatic differentiation (ForwardDiff if it's just a handful of parameters) to enable LBFGS and so on. But we have to make sure the Likelihood is differentiable in principle, but for fitting a function to a histograms that's typically not a problem.

[fhagemann]

This does not work for multithreaded code.