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



 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.

   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

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

  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
  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.

          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
 See also: fminsearch, optimset,
 (c) E.Farhi, ILL. License: EUPL.


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