gradfmu.m

matlab算法集 matlab算法集

function g = gradfmu (f,p,q,x,mu)
%-----------------------------------------------------------------------
% Usage:       g = gradfmu (f,p,q,x,mu)
%
% Description: Numerically approximate the gradient of the generalized
%              objective function F(x) using central differences.
%
%                  F(x) = f(x) + mu*(P(x) + Q(x))
%
% Inputs:       f  = name of objective function to minimize: f(x)
%               p  = name of equality constraint function: p(x) = 0
%               q  = name of inequality constraint function: q(x) >= 0
%
%                    The forms of f, p, and q are:
%
%                    function y = f(x)
%                    function u = p(x)
%                    function v = q(x)
%
%                    When f is called with n by 1 vector x, it must
%                    return the scalar y = f(x).  When p is called with 
%                    n by 1 vector x,it must compute r by 1 vector 
%                    u = p(x). When q is called with n by 1 vector x, 
%                    it must compute s by 1 vector v = q(x).
%               
%               x  = n by 1 vector of independent variables
%               mu = penalty paramter (mu >= 0)
%
% Outputs:      g = n by 1 gradient vector g(k) = dF(x)/dx(k)
%                   where:
%
%                      F(x) = f(x) + mu*(P(x) + Q(x)) 
%
%                   Here P(x) and Q(x) are the penalty terms: 
%
%                      P(x) = p'(x)p(x)
%                      Q(x) = min([0,q(x)])'min([0,q(x)])
%------------------------------------------------------------------------

% Initialize

   chkvec (x,4,'gradfmu');
   em = 0.001;
   n = length (x);
   g = zeros (n,1);

% Compute gradient

   for i = 1 : n
      x(i) = x(i) + em;
      g(i) = fmu (f,p,q,x,mu);
      x(i) = x(i) - 2*em;
      g(i) = (g(i) - fmu(f,p,q,x,mu))/(2*em);
      x(i) = x(i) + em;
   end
%------------------------------------------------------------------------