## Minimizer settings

The BornAgain minimizer interface was developed with the following ideas in mind:

• Provide an interface which looks more or less familiar for users of other Python minimization packages.
• Enable the use of our minimizer for optimization problems outside the BornAgain context.
• Allow the usage of other, possibly more advanced minimization libraries, for BornAgain fits.

Particularly, we have been inspired by the lmfit Python package, so the BornAgain setup looks very similar. In the code snippet below we give an example of finding the minimum of the Rosenbrock function using the BornAgain minimizer with default settings.

def rosenbrock(params):
x = params["x"].value
y = params["y"].value
tmp1 = y - x * x
tmp2 = 1 - x
return 100 * tmp1 * tmp1 + tmp2 * tmp2

params = ba.Parameters()

minimizer = ba.Minimizer()
result = minimizer.minimize(rosenbrock, params)
print(result.toString())

The rest of the page gives additional details on

### Fit parameter setup

The BornAgain Parameters class allows to define a collection of fit parameters which will be varied during the fit. Each fit parameter should have a unique name, starting value and possible bounds on its value.

params = ba.Parameters()
params.add("d", value=1.0, vary=False)

It is not possible to use mathematical expressions to constrain these value, as it is done in the more advanced parameter machinery of lmfit package.

### List of available minimization algorithms

The BornAgain minimizer is a wrapper around a variety of minimization engines from ROOT and GSL libraries. They are listed in the table below. By default, Minuit2/Migrad will be used and no additional configuration needs to be done.

Minimizer name Algorithm Description
Minuit2 Migrad Variable-metric method with inexact line search, a stable metric updating scheme, and checks for positive-definiteness. According to the Minuit users guide [ch. 5.1.1], this is the best minimizer for nearly all functions
Simplex Simplex method of Nelder and Mead usually, slower than Migrad, rather robust with respect to gross fluctuations in the function value, gives no reliable information about parameter errors.
Combined Minimizes with Migrad, but switches to Simplex if Migrad fails to converge.
Scan Not intended to minimize, just scans the function, one parameter at a time, retains the best value after each scan.
Fumili Optimized method for least square and log likelihood minimizations.
GSLMultiMin ConjugateFR Fletcher-Reeves conjugate gradient algorithm.
BFGS Broyden-Fletcher-Goldfarb-Shanno algorithm
BFGS2 Improved version of BFGS.
SteepestDescent Follows the downhill gradient of the function at each step.
GSLLMA Levenberg-Marquardt Algorithm
GSLSimAn Simulated Annealing Algorithm
Genetic Genetic Algorithm
Test Single-shot minimizer

To change the minimize engine and its algorithm one has to use

minimizer = ba.Minimizer()
minimizer.setMinimizer("GSLMultiMin", "BFGS2")

There are a number of minimizer options that can be changed. The commands below print the detailed info about the available minimizers, their options and the default option values.

# prints info about available minimizers
print(ba.MinimizerFactory().catalogueToString())

# prints detailed info about available minimizers and their options
print(ba.MinimizerFactory().catalogueDetailsToString())

## Minuit2 | Minuit2 minimizer from ROOT library

Algorithm names Migrad | Variable-metric method with inexact line search, best minimizer according to ROOT. Simplex | Simplex method of Nelder and Meadh, robust against big fluctuations in objective function. Combined | Combination of Migrad and Simplex (if Migrad fails). Scan | Simple objective function scan, one parameter at a time. Fumili | Gradient descent minimizer similar to Levenberg-Margquardt, sometimes can be better than all others. Default algorithm | Migrad

Options Strategy | 1 Minimization strategy (0-low, 1-medium, 2-high quality) ErrorDef | 1 Error definition factor for parameter error calculation Tolerance | 0.01 Tolerance on the function value at the minimum Precision | -1 Relative floating point arithmetic precision PrintLevel | 0 Minimizer internal print level MaxFunctionCalls | 0 Maximum number of function calls

## GSLMultiMin | MultiMin minimizer from GSL library

Algorithm names SteepestDescent | Steepest descent ConjugateFR | Fletcher-Reeves conjugate gradient ConjugatePR | Polak-Ribiere conjugate gradient BFGS | BFGS conjugate gradient BFGS2 | BFGS conjugate gradient (Version 2) Default algorithm | ConjugateFR

Options PrintLevel | 0 Minimizer internal print level MaxIterations | 0 Maximum number of iterations

## GSLLMA | Levenberg-Marquardt from GSL library

Algorithm names Default | Default algorithm

Options Tolerance | 0.01 Tolerance on the function value at the minimum PrintLevel | 0 Minimizer internal print level MaxIterations | 0 Maximum number of iterations

## GSLSimAn | Simmulated annealing minimizer from GSL library

Algorithm names Default | Default algorithm

Options PrintLevel | 0 Minimizer internal print level MaxIterations | 100 Number of points to try for each step IterationsAtTemp | 10 Number of iterations at each temperature StepSize | 1 Max step size used in random walk k | 1 Boltzmann k t_init | 50 Boltzmann initial temperature mu | 1.05 Boltzmann mu t_min | 0.1 Boltzmann minimal temperature

## Genetic | Genetic minimizer from TMVA library

Algorithm names Default | Default algorithm

Options Tolerance | 0.01 Tolerance on the function value at the minimum PrintLevel | 0 Minimizer internal print level MaxIterations | 3 Maximum number of iterations PopSize | 300 Population size RandomSeed | 0 Random seed

## Test | One-shot minimizer to test whole chain

Algorithm names Default | Default algorithm

For example, to run the Minuit minimizer with the Migrad algorithm, limit the maximum number of objective function calls and set the minimizer strategy parameter to a certain value one can use

minimizer.setMinimizer("Minuit2", "Migrad", "MaxFunctionCalls=50;Strategy=2")

### Third party minimizers

BornAgain fitting can also be done using other minimization packages. A short list of some of them is given below:

In this example we demonstrate how to use the lmfit minimizer for a typical fit of GISAS data.