Line Search Algorithm help

This part is just the background to the algorithms I am working on:

Here is the code I currently have but I'm not sure what to do to get anything to work:

function [alpha] = linesearch(nsteps)
    syms x
    f = @(x)100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
    grad = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1)); 200*(x(2)-x(1)^2)];
    gradTwo = [800*x(1)+2, -400*x(1); -400*x(2), 200];
    alpha(0) = 0;
    alpha(1) = 1;
    c1 = 10^-4;
    c2 = 0.9;
    for i = 1:nsteps
        if (f(alpha(i)) > f(0)+c1*grad(0)||(f(alpha(i)) > f(alpha(i-1))))
            alpha = lszoom(alpha(i-1), alpha(i));
            return;
        end
        if abs(grad(alpha(i))) <= abs(c2*grad(0))
            alpha = alpha(i);
            return;
        end
        if grad(alpha(i)) >= 0
            alpha = lszoom(alpha(i), alpha(i-1));
            return;
        end
        alpha(i+1) = 2*alpha;
    end
    Error('step size alpha not found within 10 iterations')
end



function [alpha] = lszoom(alphalo, alphahigh)
    syms x
    f = @(x)100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
    grad = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1)); 200*(x(2)-x(1)^2)];
    gradTwo = [800*x(1)+2, -400*x(1); -400*x(2), 200];
    alpha(0) = 0;
    alpha(1) = 1;
    c1 = 10^-4;
    c2 = 0.9;
    nsteps = 50;
    for i = 1:nsteps
        alpham = (alphalo + alphahigh) / 2;
        if (f(alpham) > alpha(0)+c1*alpham*grad(0)||f(alpham)>f(alphalo))
            alphahigh = alpham;
        else
            if abs(grad(alpham)) <= c2*abs(grad(0))
                alpha = alpham;
                return;
            end
            if grad(alpham)*(alphahigh-alphalo) >= 0
                alphahigh = alphalo;
            end
            alphalo = alpham;
        end
    end
    Error('step length alpha not found within 50 iterations')
end

Both algorithms give me the error:

"Index exceeds the number of array elements (1)

Error in sym/subsref (line 900)

R_tilde = builtin('subsref',L_tilde,Idx);

Error in lszoom (line 4)

grad = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1)); 200*(x(2)-x(1)^2)];"

[Mali Norouzi]

hi sarah, did you find the answer? i had a problem such this\:(

Answer 1

[ahmed abrous]

Hello

can you put the reference of the book please.

Regards.

Answer 2

[Daniele Mori]

Hi Sarah,

I modified your code and now it seems to work.

If you have any questions, please tell me.

Best reguards,

Daniele

syms x y
fun = 100*(y - x^2)^2 + (1 - x)^2;
d = gradient(fun);
f = matlabFunction(fun);
grad = matlabFunction(d);

x_0 = 5;
y_0 = 5;
in_point = [x_0,y_0];
s = -grad(x_0,y_0);

phi = @(alpha)f(in_point(1) + alpha*s(1),in_point(2) + alpha*s(2));
d_phi = @(alpha)grad(in_point(1) + alpha*s(1),in_point(2) + alpha*s(2))'*s;

alpha_0 = 0;
alpha_max = 1;
alpha(1) = (alpha_0 + alpha_max)/2;
c1 = 10^-4;
c2 = 0.1;

i = 1;

while 1
    if (phi(alpha(i) > phi(0)+c1*alpha(i)*d_phi(0)) || (phi(alpha(i)) > phi(alpha_0)) && i>1)
        [alpha_star,n] = lszoom(alpha_0,alpha(i),phi,d_phi);
        break;
    end
    if abs(d_phi(alpha(i))) <= abs(c2*d_phi(0))
        alpha_star = alpha(i);
        break;
    end
    if d_phi(alpha(i)) >= 0
        [alpha_star,n] = lszoom(alpha(i),alpha_0,phi,d_phi);
        break;
    end
    alpha_0 = alpha(i);
    alpha(i+1) = (alpha_0 + alpha_max)/2;
    i = i+1;
end


function [alpha_star,n] = lszoom(alphalo,alphahigh,phi,d_phi)
c1 = 10^-4;
c2 = 0.1;
n=1;
while 1
    alpham = (alphalo + alphahigh) / 2;
    if (phi(alpham) > phi(0)+c1*alpham*d_phi(0)||phi(alpham)>phi(alphalo))
        alphahigh = alpham;
    else
        if abs(d_phi(alpham)) <= -c2*d_phi(0)
            alpha_star = alpham;
            return;
        end
        if d_phi(alpham)*(alphahigh-alphalo) >= 0
            alphahigh = alphalo;
        end
        alphalo = alpham;
    end
    n = n+1;
end

end