线搜索Wolfe准则

测试：

>> [alpha, newxk, fk, newfk] = Opt_Wolfe([0 0]', [1 0]')
alpha =
    0.1250
newxk =
    0.1250
         0
fk =
     1
newfk =
    0.7900

•  代码如下：

function [alpha, newxk, fk, newfk] = Opt_Wolfe(xk, dk)
rho = 0.25; 
sigma = 0.75;
alpha = 1; 
a = 0; 
b = 1; 
while a < b
    if fun(xk + alpha*dk) <= fun(xk) + rho*alpha*gfun(xk)'*dk
        if gfun(xk + alpha*dk)'*dk >= sigma*gfun(xk)'*dk
            break;
        else
            a = alpha;
            alpha = 0.5*(a + b);
        end
    else
        b = alpha;
        alpha = (alpha+a)/2;
    end
end
newxk = xk + alpha*dk;
fk = fun(xk);
newfk = fun(newxk);

function f=fun(x)
f = 100*(x(1)^2 - x(2))^2 + (x(1)-1)^2;

function gf=gfun(x)
gf = [400*x(1)*(x(1)^2 - x(2)) + 2*(x(1) - 1);
        -200*(x(1)^2 - x(2))];