fibonacci.m

优化理论与方法的斐波那契法的matlab程序

%  Program: fibonacci.m
%  Title: Fibonacci Search
%  Description: Implements the Fibonacci search.
%   [xL1,xU1]: initial interval of uncertainty 
%  Output:
%     xs: minimum point 
%     fs: minimum value of objective function
%      k: number of iterations at convergence
%========================================================================
clear;
clc
xL1=-2;
xU1=2;
delta=0.0001;
feval=@(x) x^2+x+2;
disp(' ')
disp('Program fibonacci.m')
% Generate a Fibonacci sequence
f(1) = 1;
f(2) = 1;
while (xU1-xL1)/f(end)>=delta
      f =[f,(sum(f(end-1)+f(end)))];
end
n=numel(f);
F = f(1:n);
% Generate xa1, xb1, f(xa1), and f(xb1)
k = 1;
I1 = xU1-xL1;
I2 = (F(n-1)/F(n))*I1;
xak = xU1 - I2
xbk = xL1 + I2
fak = feval(xak);
fbk = feval(xbk);
Ik1 = I2;
xLk = xL1;
xUk = xU1;
% Perform Fibonacci search
while k < n-2 & xak <= xbk,
   Ik2 = (F(n-k-1)/F(n-k))*Ik1;
   if fak >= fbk,
      xLk1 = xak;
      xUk1 = xUk;
      xak1 = xbk;
      xbk1 = xLk1 + Ik2;
      fak1 = fbk;
      fbk1 = feval(xbk1);
      xw = 0.5*(xak1 + xUk1);
   else
      xLk1 = xLk;
      xUk1 = xbk;
      xak1 = xUk1 - Ik2;
      xbk1 = xak;
      fbk1 = fak;
      fak1 = feval(xak1);
      xw = 0.5*(xLk1 + xbk1);
   end
   xLk = xLk1;
   xUk = xUk1;
   xak = xak1
   xbk = xbk1
   fak = fak1;
   fbk = fbk1;
   Ik1 = Ik2;
   k = k + 1;
end
xs = 0.5*(xLk + xUk);
fs = feval(xs);
% Display results
format long
disp('Minimum point:')
xs
disp('Minimum value of objective function:')
fs
format short
disp('Number of iterations performed:')
k