Home > freetb4matlab > optim > minimize.m

minimize

PURPOSE ^

% [x,v,nev,...] = minimize (f,args,...) - Minimize f

SYNOPSIS ^

function [x,v,nev,varargout] = minimize (f,args,varargin)

DESCRIPTION ^

% [x,v,nev,...] = minimize (f,args,...) - Minimize f
%
% ARGUMENTS
% f    : string  : Name of function. Must return a real value
% args : list or : List of arguments to f (by default, minimize the first)
%        matrix  : f's only argument
%
% RETURNED VALUES
% x   : matrix  : Local minimum of f. Let's suppose x is M-by-N.
% v   : real    : Value of f in x0
% nev : integer : Number of function evaluations 
%     or 1 x 2  : Number of function and derivative evaluations (if
%                 derivatives are used)
% 
%
% Extra arguments are either a succession of option-value pairs or a single
% list or struct of option-value pairs (for unary options, the value in the
% struct is ignored).
% 
% OPTIONS : DERIVATIVES   Derivatives may be used if one of these options
% ---------------------   uesd. Otherwise, the Nelder-Mean (see
%                         nelder_mead_min) method is used.
% 
% 'd2f', d2f     : Name of a function that returns the value of f, of its
%                  1st and 2nd derivatives : [fx,dfx,d2fx] = feval (d2f, x)
%                  where fx is a real number, dfx is 1x(M*N) and d2fx is
%                  (M*N)x(M*N). A Newton-like method (d2_min) will be used.
%
% 'hess'         : Use [fx,dfx,d2fx] = leval (f, args) to compute 1st and
%                  2nd derivatives, and use a Newton-like method (d2_min).
%
% 'd2i', d2i     : Name of a function that returns the value of f, of its
%                  1st and pseudo-inverse of second derivatives : 
%                  [fx,dfx,id2fx] = feval (d2i, x) where fx is a real
%                  number, dfx is 1x(M*N) and d2ix is (M*N)x(M*N).
%                  A Newton-like method will be used (see d2_min).
%
% 'ihess'        : Use [fx,dfx,id2fx] = leval (f, args) to compute 1st
%                  derivative and the pseudo-inverse of 2nd derivatives,
%                  and use a Newton-like method (d2_min).
%
%            NOTE : df, d2f or d2i take the same arguments as f.
% 
% 'order', n     : Use derivatives of order n. If the n'th order derivative
%                  is not specified by 'df', 'd2f' or 'd2i', it will be
%                  computed numerically. Currently, only order 1 works.
% 
% 'ndiff'        : Use a variable metric method (bfgs) using numerical
%                  differentiation.
%
% OPTIONS : STOPPING CRITERIA  Default is to use 'tol'
% ---------------------------
% 'ftol', ftol   : Stop search when value doesn't improve, as tested by
%
%              ftol > Deltaf/max(|f(x)|,1)
%
%                 where Deltaf is the decrease in f observed in the last
%                 iteration.                                 Default=10*eps
%
% 'utol', utol   : Stop search when updates are small, as tested by
%
%              tol > max { dx(i)/max(|x(i)|,1) | i in 1..N }
%
%                 where  dx is the change in the x that occured in the last
%                 iteration.
%
% 'dtol',dtol    : Stop search when derivatives are small, as tested by
%
%              dtol > max { df(i)*max(|x(i)|,1)/max(v,1) | i in 1..N }
%
%                 where x is the current minimum, v is func(x) and df is
%                 the derivative of f in x. This option is ignored if
%                 derivatives are not used in optimization.
%
% MISC. OPTIONS
% -------------
% 'maxev', m     : Maximum number of function evaluations             <inf>
%
% 'narg' , narg  : Position of the minimized argument in args           <1>
% 'isz'  , step  : Initial step size (only for 0 and 1st order method)  <1>
%                  Should correspond to expected distance to minimum
% 'verbose'      : Display messages during execution
%
% 'backend'      : Instead of performing the minimization itself, return
%                  [backend, control], the name and control argument of the
%                  backend used by minimize. Minimimzation can then be
%                  obtained without the overhead of minimize by calling, if
%                  a 0 or 1st order method is used :
%
%              [x,v,nev] = feval (backend, args, control)
%                   
%                  or, if a 2nd order method is used :
%
%              [x,v,nev] = feval (backend, control.d2f, args, control)
%

CROSS-REFERENCE INFORMATION ^

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