min.m

利用matlab编制的利用单纯形处理工程问题的程序

function [x,fval,exitflag,output] = min(funfcn,x,options,varargin)
%MIN Multidimensional unconstrained nonlinear minimization (Nelder-Mead).
%   X = MIN(FUN,X0) starts at X0 and attempts to find a local minimizer 
%   X of the function FUN. FUN accepts input X and returns a scalar function 
%   value F evaluated at X. X0 can be a scalar, vector or matrix.
%
%   X = MIN(FUN,X0,OPTIONS)  minimizes with the default optimization
%   parameters replaced by values in the structure OPTIONS, created
%   with the OPTIMSET function.  See OPTIMSET for details.  MIN uses
%   these options: Display, TolX, TolFun, MaxFunEvals, MaxIter, FunValCheck,
%   and OutputFcn.
%
%   [X,FVAL]= MIN(...) returns the value of the objective function,
%   described in FUN, at X.
%
%   [X,FVAL,EXITFLAG] = MIN(...) returns an EXITFLAG that describes 
%   the exit condition of MIN. Possible values of EXITFLAG and the 
%   corresponding exit conditions are
%
%    1  MIN converged to a solution X.
%    0  Maximum number of function evaluations or iterations reached.
%   -1  Algorithm terminated by the output function.
%
%   [X,FVAL,EXITFLAG,OUTPUT] = MIN(...) returns a structure
%   OUTPUT with the number of iterations taken in OUTPUT.iterations, the
%   number of function evaluations in OUTPUT.funcCount, the algorithm name 
%   in OUTPUT.algorithm, and the exit message in OUTPUT.message.
%
%   Examples
%     FUN can be specified using @:
%        X = min(@sin,3)
%     finds a minimum of the SIN function near 3.
%     In this case, SIN is a function that returns a scalar function value
%     SIN evaluated at X.
%
%     FUN can also be an anonymous function:
%        X = min(@(x) norm(x),[1;2;3])
%     returns a point near the minimizer [0;0;0].
%
%   If FUN is parameterized, you can use anonymous functions to capture the 
%   problem-dependent parameters. Suppose you want to optimize the objective     
%   given in the function MYFUN, which is parameterized by its second argument A. 
%   Here MYFUN is an M-file function such as
%
%     function F = myfun(x,a)
%     f = x(1)^2 + a*x(2)^2;
%
%   To optimize for a specific value of A, first assign the value to A. Then 
%   create a one-argument anonymous function that captures that value of A 
%   and calls MYFUN with two arguments. Finally, pass this anonymous function 
%   to FMISEARCH:
%    
%     a = 1.5; % define parameter first
%     x = min(@(x) myfun(x,a),[0.3;1])



defaultopt = struct('Display','notify','MaxIter','200*numberOfVariables',...
    'MaxFunEvals','200*numberOfVariables','TolX',1e-4,'TolFun',1e-4, ...
    'FunValCheck','off','OutputFcn',[]);

% If just 'defaults' passed in, return the default options in X
if nargin==1 && nargout <= 1 && isequal(funfcn,'defaults')
    x = defaultopt;
    return
end

if nargin < 2,
    error('MATLAB:min:NotEnoughInputs',...
        'MIN requires at least two input arguments');
end

if nargin<3, options = []; end

% Check for non-double inputs
if ~isa(x,'double')
  error('MATLAB:min:NonDoubleInput', ...
         'MIN only accepts inputs of data type double.')
end

n = numel(x);
numberOfVariables = n;

printtype = optimget(options,'Display',defaultopt,'fast');
tolx = optimget(options,'TolX',defaultopt,'fast');
tolf = optimget(options,'TolFun',defaultopt,'fast');
maxfun = optimget(options,'MaxFunEvals',defaultopt,'fast');
maxiter = optimget(options,'MaxIter',defaultopt,'fast');
funValCheck = strcmp(optimget(options,'FunValCheck',defaultopt,'fast'),'on');

% In case the defaults were gathered from calling: optimset('min'):
if ischar(maxfun)
    if isequal(lower(maxfun),'200*numberofvariables')
        maxfun = 200*numberOfVariables;
    else
        error('MATLAB:min:OptMaxFunEvalsNotInteger',...
            'Option ''MaxFunEvals'' must be an integer value if not the default.')
    end
end
if ischar(maxiter)
    if isequal(lower(maxiter),'200*numberofvariables')
        maxiter = 200*numberOfVariables;
    else
        error('MATLAB:min:OptMaxIterNotInteger',...
            'Option ''MaxIter'' must be an integer value if not the default.')
    end
end

switch printtype
    case 'notify'
        prnt = 1;
    case {'none','off'}
        prnt = 0;
    case 'iter'
        prnt = 3;
    case 'final'
        prnt = 2;
    case 'simplex'
        prnt = 4;
    otherwise
        prnt = 1;
end
% Handle the output
outputfcn = optimget(options,'OutputFcn',defaultopt,'fast');
if isempty(outputfcn)
    haveoutputfcn = false;
else
    haveoutputfcn = true;
    xOutputfcn = x; % Last x passed to outputfcn; has the input x's shape
    % Convert to function handle as needed.
    outputfcn = fcnchk(outputfcn,length(varargin));
end

header = ' Iteration   Func-count     min f(x)         Procedure';

% Convert to function handle as needed.
funfcn = fcnchk(funfcn,length(varargin));
% Add a wrapper function to check for Inf/NaN/complex values
if funValCheck
    % Add a wrapper function, CHECKFUN, to check for NaN/complex values without
    % having to change the calls that look like this:
    % f = funfcn(x,varargin{:});
    % x is the first argument to CHECKFUN, then the user's function,
    % then the elements of varargin. To accomplish this we need to add the 
    % user's function to the beginning of varargin, and change funfcn to be
    % CHECKFUN.
    varargin = {funfcn, varargin{:}};
    funfcn = @checkfun;
end

n = numel(x);

% Initialize parameters
rho = 1; chi = 2; psi = 0.5; sigma = 0.5;
onesn = ones(1,n);
two2np1 = 2:n+1;
one2n = 1:n;

% Set up a simplex near the initial guess.
xin = x(:); % Force xin to be a column vector
v = zeros(n,n+1); fv = zeros(1,n+1);
v(:,1) = xin;    % Place input guess in the simplex! (credit L.Pfeffer at Stanford)
x(:) = xin;    % Change x to the form expected by funfcn
fv(:,1) = funfcn(x,varargin{:});
func_evals = 1;
itercount = 0;
how = '';

% Initialize the output function.
if haveoutputfcn
    [xOutputfcn, optimValues, stop] = callOutputFcn(outputfcn,x,xOutputfcn,'init',itercount, ...
        func_evals, how, fv(:,1),varargin{:});
    if stop
        [x,fval,exitflag,output] = cleanUpInterrupt(xOutputfcn,optimValues);
        if  prnt > 0
            disp(output.message)
        end
        return;
    end
end

% Print out initial f(x) as 0th iteration
if prnt == 3
    disp(' ')
    disp(header)
    disp(sprintf(' %5.0f        %5.0f     %12.6g         %s', itercount, func_evals, fv(1), how));
elseif prnt == 4
    clc
    formatsave = get(0,{'format','formatspacing'});
    format compact
    format short e
    disp(' ')
    disp(how)
    v
    fv
    func_evals
end
% OutputFcn call
if haveoutputfcn
    [xOutputfcn, optimValues, stop] = callOutputFcn(outputfcn,x,xOutputfcn,'iter',itercount, ...
        func_evals, how, fv(:,1),varargin{:});
    if stop  % Stop per user request.
        [x,fval,exitflag,output] = cleanUpInterrupt(xOutputfcn,optimValues);
        if  prnt > 0
            disp(output.message)
        end
        return;
    end
end

% Following improvement suggested by L.Pfeffer at Stanford
usual_delta = 0.05;             % 5 percent deltas for non-zero terms
zero_term_delta = 0.00025;      % Even smaller delta for zero elements of x
for j = 1:n
    y = xin;
    if y(j) ~= 0
        y(j) = (1 + usual_delta)*y(j);
    else
        y(j) = zero_term_delta;
    end
    v(:,j+1) = y;
    x(:) = y; f = funfcn(x,varargin{:});
    fv(1,j+1) = f;
end

% sort so v(1,:) has the lowest function value
[fv,j] = sort(fv);
v = v(:,j);

how = 'initial simplex';
itercount = itercount + 1;
func_evals = n+1;
if prnt == 3
    disp(sprintf(' %5.0f        %5.0f     %12.6g         %s', itercount, func_evals, fv(1), how))
elseif prnt == 4
    disp(' ')
    disp(how)
    v
    fv
    func_evals
end
% OutputFcn call
if haveoutputfcn
    [xOutputfcn, optimValues, stop] = callOutputFcn(outputfcn,x,xOutputfcn,'iter',itercount, ...