% Homework ：Steepst Decent Methed % f(x1,x2)=(x1-2)^4+(x1-2*x2)^2 % x0=[0;3] % Partial_x1 = 4*(x1-2)^3+2*(x1-2*x2); % Partial_x2 = 4*(2*x2-x1); % Alpha = (f1*(x1-2)+(f1-2*f2)*(x1-2*x2))/(f1^2+(f1-2*f2)^2) clear all clc x0=[0;3]; maxiter=50; f1=4*(x0(1)-2)^3+2*(x0(1)-2*x0(2)); f2=4*(2*x0(2)-x0(1)); d0=-[f1;f2]; alpha=(f1*(x0(1)-2)+(f1-2*f2)*(x0(1)-2*x0(2)))/(f1^2+(f1-2*f2)^2); %x(:,1)=x0+alpha*d0; x(:,1)=x0; x(:,2)=x0+alpha*d0; % x(:,2) = x1 k=2; d(:,1)=d0; f=zeros(maxiter,1); while k < maxiter && norm(d(:,k-1)) > 1e-8 f1=4*(x(1,k)-2)^3+2*(x(1,k)-2*x(2,k)); f2=4*(2*x(2,k)-x(1,k)); d(:,k)=-[f1;f2]; alpha=(f1*(x(1,k)-2)+(f1-2*f2)*(x(1,k)-2*x(2,k)))/(f1^2+(f1-2*f2)^2); x(:,k+1)=x(:,k)+alpha*d(:,k); fun_val=(x(1,k)-2)^4+(x(1,k)-2*x(2,k))^2; f(k)=fun_val; fprintf('k=%3d norm_grad=%2.6f fun_val=%2.6f\n', k,norm(d(:,k)),fun_val); semilogy(f(1:k),'LineWidth',2); %axis equal xlabel('Interation Number'); ylabel('Objective Funtion Value'); %drawnow; pause(0.2); k=k+1; end figure [X1,X2]=meshgrid(-4:0.01:4,-4:0.01:4); F=(X1-2).^4+(X1-2*X2).^2; contour(X1,X2,F,20); text(x0(1),x0(2),'X^0','FontSize',18); hold on semilogy(x(1,:),x(2,:),'-ko','MarkerSize',10,'LineWidth',2); %set(gca,'FontSize',16); %axis equal text(2,1,'x^*','FontSize',18); title('Steepest Descent Method a=0.01');

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