下面是 armijo线搜索+最速下降法的小程序，matlab用的很不熟，费了不少劲。

函数：

function g=fun_obj(x)syms a bf = 1/2*a^2+b^2-a*b-2*a;a=x(1);b=x(2);g=eval(f);

求梯度：

function g=fun_grad(x)syms a bf = 1/2*a^2+b^2-a*b-2*a;gradient = jacobian(f,[a,b]);a = x(1);b = x(2);g = eval(gradient);

armijo线搜索：

function mk = armijo( xk, rho, sigma, d )assert( rho > 0 && rho < 1 );assert( sigma > 0 && sigma < 0.5 );mk = 0; max_mk = 100;while mk <= max_mk    x = xk + rho^mk * d;    if fun_obj( x ) <=  fun_obj( xk ) + sigma * rho^mk *fun_grad(xk)*d';        break;    end    mk = mk + 1;endreturn;

主程序：

function result = armijograd(x0)max_iter = 5000;    % max number of iterationsEPS = 1e-6;         % threshold of gradient norm            rho = 0.45; sigma = 0.2;   % Armijo parametersk = 0; xk = x0; % initializationwhile k < max_iter        k = k + 1;        dk =  fun_grad( xk );      % gradient vector    d = -1 * dk;               % search direction        if norm( dk ) < EPS        %precision        break;    end        mk = armijo( xk, rho, sigma, d);   %armijo line search        xk = xk + rho^mk * d;              %updateend    result = xk;   return;

最终结果是：[4,2]';程序正确。