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12 Nov 2001 (Updated )

Multi Input Multi Output Systems Toolbox

function [X,OPTIONS,lambda,HESSIAN]=constr(FUN,X,OPTIONS,VLB,VUB,GRADFUN,varargin)

%CONSTR Finds the constrained minimum of a function of several variables.
%   This is a wrapper for FMINCON inside mimotool/jtools
%   X=CONSTR('FUN',X0) starts at X0 and finds a constrained minimum to 
%   the function which is described in FUN (usually an M-file: FUN.M).
%   The function 'FUN' should return two arguments: a scalar value of the 
%   function to be minimized, F, and a matrix of constraints, G: 
%   [F,G]=FUN(X). F is minimized such that G <= zeros(size(G)).
%   X=CONSTR('FUN',X,OPTIONS) allows a vector of optional parameters to 
%   be defined. For more information type HELP FOPTIONS.
%   X=CONSTR('FUN',X,OPTIONS,VLB,VUB) defines a set of lower and upper
%   bounds on the design variables, X, so that the solution is always in 
%   the range VLB <= X <= VUB. 
%   X=CONSTR('FUN',X,OPTIONS,VLB,VUB,'GRADFUN') allows a function 
%   'GRADFUN' to be entered which returns the partial derivatives of the 
%   function and the constraints at X:  [gf,GC] = GRADFUN(X).
%   Use OPTIONS(9)=1 to check analytic gradients in GRADFUN against
%   numeric gradients during the first iteration.
%   X=CONSTR('FUN',X,OPTIONS,VLB,VUB,'GRADFUN',P1,P2,...) passes the 
%   problem-dependent parameters P1,P2,... directly to the functions FUN 
%   and GRADFUN: FUN(X,P1,P2,...) and GRADFUN(X,P1,P2,...).  Pass
%   empty matrices for OPTIONS, VLB, VUB, and 'GRADFUN' to use the 
%   default values.
%   [X,OPTIONS]=CONSTR('FUN',X0,...) returns the parameters used in the 
%   optimization method.  For example, OPTIONS(10) contains the number 
%   of function evaluations used.
%   [X,OPTIONS,LAMBDA]=CONSTR('FUN',X0,...) returns the Lagrange multipliers
%   at the solution X in the vector LAMBDA.
%   [X,OPTIONS,LAMBDA,HESS]=CONSTR('FUN',X0,...) returns the quasi-Newton
%   approximation to the Hessian matrix at the solution X.
%   extra parameters, P1, P2, ... to be passed directly to FUN:
%   [F,G]=FUN(X,P1,P2,...). Empty arguments ([]) are ignored.

if nargin < 2, error('constr requires two input arguments'); end
if nargin < 3, OPTIONS=[]; end
if nargin < 4, VLB=[]; end
if nargin < 5, VUB=[]; end
if nargin < 6, GRADFUN=[]; end

if ~isempty(OPTIONS),
   if OPTIONS(1), 

str='[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = fmincon(FUN,X,[],[],[],[],VLB,VUB,[],options'; 
if ~isempty(varargin),
   for i=1:length(varargin),
      str=[str ',varargin{' num2str(i) '}'];
str=[str ');'];


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