最优化——FR共轭梯度法matlab程序

% cg.m

function [x, output] = cg(fun, dfun, x0)

% fun: character variable, the name of function computing objective function

% dfun: character variable, the name of function computing the gradient of objective function

% x0: real vector, input initial point

% x :real vector, output solution

% output: structure variable, output the value of f, the number ofiteration, the number of function evaluations and the norm of gradient at last point x

%

% Step 1: initialization

%

epsi = 1.0e-3; % termination tolenrence

k = 0; % the number of iteration

funcN = 0; % the number of function evaluation

rho = 0.01; l = 0.15; u = 0.85;

x = x0;

f = feval(fun, x);

funcN = funcN + 1;

n = length(x0);

%

% Step 2: check convergence condition

%

g = feval(dfun, x);

while norm(g) > epsi & k <= 150

%

% Step 3: form search direction

%

iterm = k - floor(k/(n+1))*(n+1);

iterm = iterm + 1;

k = k + 1;

if iterm == 1

d = -g;

gd = g'*d;

else

beta = g'*g/(gold'*gold);

d = -g + beta*dold;

gd = g'*d;

if gd >= 0.0

d = -g; gd = g' *d;

end

end

%

% Step 4: line search

%

alpha_0 = 1.0;

[alpha, funcNk, exitflag] = lines(fun, rho, l, u, alpha_0, f, gd, x, d);

funcN = funcN + funcNk;

if exitflag == -1

break;

end

%

% Step 5: compute new point

%

s = alpha*d; x = x + s;

f = feval(fun, x);

funcN = funcN + 1;

gold = g;

dold = d;

g = feval(dfun, x);

k = k + 1;

end

%

% Step 6: output

%

output.fval = f;

output.iteration = k;

output.funcount = funcN;

output.gnorm = norm(g);

end

测试

% f1.m

function f = f1(x)

% objective function

f = (x(2)-x(1)^2)^2+(1-x(1))^2;

end

% df1.m

function g = df1(x)

% grads function

g = [4.0*(x(1)^3-x(1)*x(2))+2*x(1)-2;2.0*(x(2)-x(1)^2)];

end

% Command

x0=[-1.9;2];

x=cg('f1', 'df1', x0)

结果

x =

1.0007

1.0019