考虑无约束优化问题f（x)=100（x-x2）2+（x1-1)2，设当前迭代点x=（-1,1)，下降方向d2=(1,-2)T，试用非精确的Armijo搜索准则、Wolfe搜索准则、强Wolfe 搜索准则求解步长a的matlab程序

非精确的Armijo搜索准则：

function a = armijo(f, x, d)
    sigma = 0.5;
    beta = 0.5;
    a = 1;
    while f(x + a*d) > f(x) + beta*a*grad(f, x)'*d
        a = sigma*a;
    end
end

function g = grad(f, x)
    h = 1e-6;
    n = length(x);
    g = zeros(n, 1);
    for i = 1:n
        e = zeros(n, 1);
        e(i) = 1;
        g(i) = (f(x+h*e) - f(x-h*e)) / (2*h);
    end
end

% main function
f = @(x) 100*(x(1)-x(1)^2)^2 + (x(2)-1)^2;
x = [-1;1];
d = [1;-2];
a = armijo(f, x, d)

Wolfe搜索准则：

function a = wolfe(f, x, d)
    sigma = 0.5;
    rho = 0.1;
    a = 1;
    while true
        if f(x + a*d) > f(x) + rho*a*grad(f, x)'*d
            a = sigma*a;
        elseif grad(f, x + a*d)'*d < rho*grad(f, x)'*d
            a = sigma*a;
        else
            break;
        end
    end
end

% main function
f = @(x) 100*(x(1)-x(1)^2)^2 + (x(2)-1)^2;
x = [-1;1];
d = [1;-2];
a = wolfe(f, x, d)

强Wolfe搜索准则：

function a = strong_wolfe(f, x, d)
    sigma = 0.5;
    rho = 0.1;
    a = 1;
    while true
        fx = f(x);
        g = grad(f, x);
        if f(x + a*d) > fx + rho*a*g'*d
            a = zoom(f, x, d, a, fx, g'*d, rho, sigma);
            break;
        elseif abs(g(f, x + a*d)'*d) <= -rho*g'*d
            break;
        elseif g(f, x + a*d)'*d >= 0
            a = zoom(f, x, d, a, fx, g'*d, rho, sigma);
            break;
        else
            a = sigma*a;
        end
    end
end

function a = zoom(f, x, d, a_lo, f_lo, g_lo_d, rho, sigma)
    a_hi = 2*a_lo;
    while true
        a = (a_lo + a_hi) / 2;
        f_val = f(x + a*d);
        if f_val > f_lo + rho*a*g_lo_d || f_val >= f(x + a_lo*d)
            a_hi = a;
        else
            g = grad(f, x + a*d);
            if abs(g'*d) <= -rho*g_lo_d
                break;
            elseif g'*d*(a_hi - a_lo) >= 0
                a_hi = a_lo;
                a_lo = a;
            else
                a_lo = a;
            end
        end
    end
end

% main function
f = @(x) 100*(x(1)-x(1)^2)^2 + (x(2)-1)^2;
x = [-1;1];
d = [1;-2];
a = strong_wolfe(f, x, d)