MATLAB拟牛顿算法BFGS代码及应用实例

function [xk,oldf,history] = BFGS(func,xk,epsilon,iter) % quasi-Newton method oldf = feval(func,xk); % begin n = length(xk); Bk = eye(n);% hessian grad = fgrad(func,xk); % gradient for t = 1:iter dk = -Bk\grad; % direction ak = armijo(func,xk,dk,grad);% step new_xk = xk + ak*dk'; newf = feval(func,new_xk); new_grad = fgrad(func,new_xk); % gradient if(norm(grad)<epsilon) break; end yk = new_grad - grad; sk = new_xk' - xk'; if(yk'*sk>0) Bk = Bk - (Bk*sk*sk'*Bk)/(sk'*Bk*sk) + (yk*yk')/(yk'*sk); end xk = new_xk; oldf = newf; grad = new_grad; history(t)=oldf; fprintf('iter=%d ObjVal=%g\n',t,oldf); end end