Line Search Algorithm help

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Sarah Johnson
Sarah Johnson 2020-2-20
编辑： Daniele Mori 2023-4-21
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)];"
  1 个评论
Mali Norouzi
Mali Norouzi 2021-6-23
hi sarah, did you find the answer? i had a problem such this\:(

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回答（2 个）

ahmed abrous
ahmed abrous 2022-5-16
Hello
can you put the reference of the book please.
Regards.
Daniele Mori
Daniele Mori 2023-4-21
编辑：Daniele Mori 2023-4-21
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

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