Find the minimum of a function using Steepest Descent Method

I build this code for find the minimum of a function and draw the graph according to the method. But there are some bugs which I cannot solve. I will attach a similar graph also. Hope to have some corrections on this code. )

Thank you.

%steepest descent method
clc
clear

func = @(x) 10.*x(1).^2 - 4.*x(1).*x(2) + 7.*x(2).^2 - 4.* sqrt5 (5.*x(1) - x(2)) - 16 ;

e = 0.01; %accuracy
i=0; %number of iterations
n=0; %number of calculated objective function values

H = [20 -4 ; -4 14];
n = n + 4;
b = [-20*sqrt(5); 4*sqrt(5)];
c = -16 ;
x =[0 10]';

Xmin=-inv(H)*b;
F= x'*H*x/2+x'*b+c;
n = n + 1;
antiGrad= -(H*x+b);
n = n + 2;
norm_aG = norm(antiGrad);

Points(:,i+1)=x;
func(1)=F;
while norm_aG>e
    i=i+1;
    kappa = norm_aG^2/dot(H*antiGrad,antiGrad);
    x=x+kappa*antiGrad;
    F= x'*H*x/2+x'*b+c;
    n=n+1;
    antiGrad= -(H*x+b);
    n=n+2;
    norm_aG = norm(antiGrad);
    Points(:,i+1)=x;
    func(i+1)=F;
end

function I = drawGraph(Xmin, Points, func)
X=linspace(Xmin(1)-5,Xmin(1)+5);
Y=linspace(Xmin(2)-5,Xmin(2)+5);
grid on
hold on
box on
xlabel('X');
ylabel('Y');
xmin=min(Points(1,:))-5;
xmax=max(Points(1,:))+5;
ymin=min(Points(2,:))-5;
ymax=max(Points(2,:))+5;
u=linspace(xmin, xmax);
v=linspace(ymin, ymax);
[XX, YY] = meshgrid(u,v);
I = XX.^2.*10 - 4.*XX.*YY + 7.*YY.^2 - 4.*sqrt(5).*(5*XX-YY) -  44;
contour(XX, YY, I, func,'r', 'showText', 'on');
plot(Points(1,:), Points(2, :), 'b-*');
end


fprintf('Precision parameter %.2f\n',e);

Function definitions in a script must appear at the end of the file.
Move all statements after the "drawGraph" function definition to before the first local function definition.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON

fprintf('point of minimum: [%.2f ,%.2f]\n', x(1),x(2));
fprintf('Min: %10.2f \n', F);
fprintf('Iterations: %d \n',i );
fprintf('number of calculated objective function values: %d\n\n',n );

Answer 1

[Walter Roberson]

Your

function I = drawGraph

definition ends at the end after plot(Points(1,:), Points(2, :), 'b-*'); . Your lines displaying the minimum and so on are not within any function definition. Those lines should be moved to before the function statement.

[Janidu]

sorry I tried many times and keep getting more more errors.(

[Walter Roberson]

%steepest descent method

func = @(x) 10.*x(1).^2 - 4.*x(1).*x(2) + 7.*x(2).^2 - 4.* sqrt5 (5.*x(1) - x(2)) - 16 ;

e = 0.01; %accuracy
i=0; %number of iterations
n=0; %number of calculated objective function values

H = [20 -4 ; -4 14];
n = n + 4;
b = [-20*sqrt(5); 4*sqrt(5)];
c = -16 ;
x =[0 10]';

Xmin=-inv(H)*b;
F= x'*H*x/2+x'*b+c;
n = n + 1;
antiGrad= -(H*x+b);
n = n + 2;
norm_aG = norm(antiGrad);

Points(:,i+1)=x;
funcvalues(1)=F;
while norm_aG>e
    i=i+1;
    kappa = norm_aG^2/dot(H*antiGrad,antiGrad);
    x=x+kappa*antiGrad;
    F= x'*H*x/2+x'*b+c;
    n=n+1;
    antiGrad= -(H*x+b);
    n=n+2;
    norm_aG = norm(antiGrad);
    Points(:,i+1)=x;
    funcvalues(i+1)=F;
end


fprintf('Precision parameter %.2f\n',e);

Precision parameter 0.01

fprintf('point of minimum: [%.2f ,%.2f]\n', x(1),x(2));

point of minimum: [2.24 ,0.00]

fprintf('Min: %10.2f \n', F);

Min:     -66.00 

fprintf('Iterations: %d \n',i );

Iterations: 8 

fprintf('number of calculated objective function values: %d\n\n',n );

number of calculated objective function values: 31

drawGraph(x, Points, funcvalues);

function I = drawGraph(Xmin, Points, func)
X=linspace(Xmin(1)-5,Xmin(1)+5);
Y=linspace(Xmin(2)-5,Xmin(2)+5);
grid on
hold on
box on
xlabel('X');
ylabel('Y');
xmin=min(Points(1,:))-5;
xmax=max(Points(1,:))+5;
ymin=min(Points(2,:))-5;
ymax=max(Points(2,:))+5;
u=linspace(xmin, xmax);
v=linspace(ymin, ymax);
[XX, YY] = meshgrid(u,v);
I = XX.^2.*10 - 4.*XX.*YY + 7.*YY.^2 - 4.*sqrt(5).*(5*XX-YY) -  44;
contour(XX, YY, I, func,'r', 'showText', 'on');
plot(Points(1,:), Points(2, :), 'b-*');
end

[Janidu]

ohh thank you very much!! Understood!!

[Walter Roberson]

Your func appears to be unused ??

[Janidu]

Yes earlier. Now there is a warning in 36th line. But code is running. )