Avoiding local minima - alternative minimization algorithms

ngedik

Hello,
I am trying to fit five parameters which define the sample contribution to the peak shape. The following is an excerpt of my code:
`
prm pr1 0.007 min 0
prm pr2 0.007 min 0
prm pr3 0.007 min 0
prm pr4 0.007 min 0
prm pr5 0.007 min 0

lor_fwhm = pr1 Tan(Th) + pr2/Cos(Th) ;
gauss_fwhm = ( pr3 Tan²(Th) + pr4 Tan(Th) + pr5 )^1/2 ;
`

When I refine these five parameters, I observe that the fit quality depends on the initial values I pick. Some initial values converge to good fits, while slightly different initial values converge to worse fits. I believe the minimization algorithm is getting stuck in local minima. Are there alternative minimization algorithms I could employ to be less sensitive to initial values and improve the chance of reaching a global minimum?

rowlesmr

You can try adding some simulated annealing. Provide some max and min values to your parameters, and TOPAS will jiggle them around trying to find the global minimum

ngedik

rowlesmr Thank you for the suggestion. This worked fine. I found good values for the above empirical peak shape parameters (as well as TCHZ parameters) and for many other profile parameters.

johnsoevans

In addition to Matthew's comment:
If you're using this as a purely empirical peak shape then you might allow pr values to go negative.
You could also look at topas.inc to see some of the "tricks" used to help convergence of peak shape functions. For example with the TCHZ peak shape min/max values are set as below. The "del" controls changes to parameters (see Tech Ref for details).

If_Prm_Eqn_Rpt(u, uv, min = Max(-1, Val-.1); max = Min(2, Val+.1); del 1.0e-4)

ngedik

johnsoevans Thank you for pointing this out.