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iFit/fmincmaes

PURPOSE ^

[MINIMUM,FVAL,EXITFLAG,OUTPUT] = FMINCMAES(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) Evolution Strategy with Covariance Matrix Adaption

SYNOPSIS ^

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

DESCRIPTION ^

 [MINIMUM,FVAL,EXITFLAG,OUTPUT] = FMINCMAES(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) Evolution Strategy with Covariance Matrix Adaption

 CMAES implements an Evolution Strategy with Covariance Matrix
 Adaptation (CMA-ES) for nonlinear function minimization.
 The CMA-ES (Evolution Strategy with Covariance
 Matrix Adaptation) is a robust search method which should be
 applied, if derivative based methods, e.g. quasi-Newton BFGS or
 conjucate gradient, (supposably) fail due to a rugged search
 landscape (e.g. noise, local optima, outlier, etc.). On smooth
 landscapes CMA-ES is roughly ten times slower than BFGS. For up to
 N=10 variables even the simplex direct search method (Nelder & Mead)
 is often faster, but far less robust than CMA-ES.

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

 Example:
   banana = @(x)100*(x(2)-x(1)^2)^2+(1-x(1))^2;
   [x,fval] = fmincmaes(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=fmincmaes('defaults');
  options.PopulationSize sets the population size (20-40).
  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.

 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.

 References
 Hansen, N. and S. Kern (2004). Evaluating the CMA Evolution Strategy on 
   Multimodal Test Functions.  Eighth International Conference on Parallel 
   Problem Solving from Nature PPSN VIII, Proceedings, pp. 282-291, Springer. 
 Hansen, N. and A. Ostermeier (2001). Completely Derandomized Self-Adaptation 
   in Evolution Strategies. Evolutionary Computation, 9(2), pp. 159-195.
 Hansen, N., S.D. Mueller and P. Koumoutsakos (2003). Reducing the Time 
   Complexity of the Derandomized Evolution Strategy with Covariance Matrix 
   Adaptation (CMA-ES). Evolutionary Computation, 11(1). 

 Contrib:
 Nikolaus Hansen, 2001-2007. e-mail: hansen@bionik.tu-berlin.de [cmaes]

 Version: Mar. 22, 2017
 See also: fminsearch, optimset
 (c) E.Farhi, ILL. License: EUPL.

CROSS-REFERENCE INFORMATION ^

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