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[MINIMUM,FVAL,EXITFLAG,OUTPUT] = fminsimpsa(FUN,PARS,[OPTIONS],[CONSTRAINTS]) simplex/simulated annealing


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


 [MINIMUM,FVAL,EXITFLAG,OUTPUT] = fminsimpsa(FUN,PARS,[OPTIONS],[CONSTRAINTS]) simplex/simulated annealing

 fminsimpsa finds a minimum of a function of several variables using an algorithm 
 that is based on the combination of the non-linear simplex and the simulated 
 annealing algorithm (the SIMPSA algorithm, Cardoso et al., 1996). 
 In this paper, the algorithm is shown to be adequate for the global optimi-
 zation of an example set of unconstrained and constrained NLP functions.
   fminsimpsa(fun, pars) asks to minimize the 'fun' objective function with starting
     parameters 'pars' (vector)
   fminsimpsa(fun, pars, options) same as above, with customized options (optimset)
   fminsimpsa(fun, pars, options, fixed) 
     is used to fix some of the parameters. The 'fixed' vector is then 0 for
     free parameters, and 1 otherwise.
   fminsimpsa(fun, pars, options, lb, ub) 
     is used to set the minimal and maximal parameter bounds, as vectors.
   fminsimpsa(fun, pars, options, constraints) 
     where constraints is a structure (see below).
   fminsimpsa(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
   fminsimpsa(..., args, ...)
     sends additional arguments to the objective function
       criteria = FUN(pars, args, ...)

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

 Reference: Section 10.4 and 10.9 in "Numerical Recipes in C", ISBN 0-521-43108-5
   Cardoso, Salcedo, Feyo de Azevedo and Bardosa, Comp. Chem Engng, 21 (1997) 1349
   Kirkpatrick, J. Stat. Phys. 34 (1984) 975.
 Contrib:   2006 Brecht Donckels, BIOMATH, brecht.donckels@ugent.be
 Systems Biology Toolbox for MATLAB, 2005 Henning Schmidt, FCC, henning@fcc.chalmers.se [SIMPSA]
 (c) E.Farhi, ILL. License: EUPL.


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