Home > Libraries > Optimizers > fmin.m

# iFit/fmin

## PURPOSE

[MINIMUM,FVAL,EXITFLAG,OUTPUT] = FMIN(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) Best optimizer

## SYNOPSIS

function [pars,fval,exitflag,output] = fmin(varargin)

## DESCRIPTION

``` [MINIMUM,FVAL,EXITFLAG,OUTPUT] = FMIN(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) Best optimizer

This minimization method is determined automatically from the objective function
behaviour and number of free parameters. You can however force a specific
optimizer by setting e.g. options.optimizer='fminpso'

WARNING: as the selected optimizer may change from one call to an other, the
solution found may vary as well. To avoid that, rather use a specific optimizer.

Best optimizers are:
fminpso:    Particle Swarm Optimization
fminpowell: Powell with Coggins line search
fminhooke:  Hooke-Jeeves direct search
fminralg:   Shor R-algorithm
fminsimpsa: Simplex/simulated annealing
fminimfil:  Unconstrained Implicit filtering
Type <a href="matlab:doc(iData,'Optimizers')">doc(iData,'Optimizers')</a> to access the Optimizers Documentation.

Calling:
fmin(fun, pars) asks to minimize the 'fun' objective function with starting
parameters 'pars' (vector)
fmin(fun, pars, options) same as above, with customized options (optimset)
fmin(fun, pars, options, fixed)
is used to fix some of the parameters. The 'fixed' vector is then 0 for
free parameters, and 1 otherwise.
fmin(fun, pars, options, lb, ub)
is used to set the minimal and maximal parameter bounds, as vectors.
fmin(fun, pars, options, constraints)
where constraints is a structure (see below).
fmin(problem) where problem is a structure with fields
problem.objective:   function to minimize
problem.x0:          starting parameter values
problem.options:     optimizer options (see below)
problem.constraints: optimization constraints
fmin(..., args, ...)
sends additional arguments to the objective function
criteria = FUN(pars, args, ...)

The options structure may contain the following members, in agreement with 'optimset':
options.Display: Level of display [ off | iter | notify | final ]. Default is 'off'
options.MaxFunEvals: Maximum number of function evaluations allowed, sometimes referred as the 'cost' or 'budget'.
options.MaxIter: Maximum number of iterations allowed
options.TolFun: Termination tolerance on the function value (absolute value or change). Use 'x%' to specify a relative function change.
options.TolX: Termination tolerance on parameter change. Use 'x%' to specify a relative parameter change.
options.OutputFcn: Name of an output function. When set, it is called at each iteration step. You may use 'fminplot', which is provided in Optimizers. Refer to the Fit page for more information about fminplot. A simpler/faster alternative is the 'fminstop' option.
options.PlotFcns: same as OutputFcn, but can be a set of function in a cell array.
options.FunValCheck: Check for invalid values, such as NaN or complex
options.MinFunEvals: when set, waits for a given number of iterations before testing for convergence
options.optimizer: the optimizer to use

Example:
banana = @(x)100*(x(2)-x(1)^2)^2+(1-x(1))^2;
[x,fval] = fmin(banana,[-1.2, 1])

Input:
FUN is the function to minimize (handle or string): criteria = FUN(PARS)
It needs to return a single value or vector.

PARS is a vector with initial guess parameters. You must input an
initial guess. PARS can also be given as a single-level structure.

OPTIONS is a structure with settings for the optimizer,
compliant with optimset. Default options may be obtained with
o=fmin('defaults')
options.MinFunEvals sets the minimum number of function evaluations to reach
An empty OPTIONS sets the default configuration.

CONSTRAINTS may be specified as a structure
constraints.min= vector of minimal values for parameters
constraints.max= vector of maximal values for parameters
constraints.fixed= vector having 0 where parameters are free, 1 otherwise
constraints.step=  vector of maximal parameter changes per iteration
constraints.eval=  expression making use of 'p', 'constraints', and 'options'
and returning modified 'p'
or function handle p=@constraints.eval(p)
When given as a vector of 0,1, CONSTRAINTS indicate which parameters
are fixed.
An empty CONSTRAINTS sets no constraints.

Additional arguments are sent to the objective function.

Output:
MINIMUM is the solution which generated the smallest encountered
value when input into FUN.
FVAL is the value of the FUN function evaluated at MINIMUM.
EXITFLAG return state of the optimizer
OUTPUT additional information returned as a structure.

Version: Nov. 26, 2018