# Question:Method of Steepest Descent Algorithm

## Question:Method of Steepest Descent Algorithm

Maple

I need to create an iterative code to find the minimum of the function

f(x)=1/2*Transpose(x)*A*x-Transpose(x)*b

where x and b are vectors in R^2 and A is a 2X2 symmetric positive definite matrix. The implications of this is that the gradient of the function is

and that we are indeed searching for a minimum.

This is the code I have so far, using the while command to create a loop.

SteepestDescent := proc (A, b) local x, r, k, a;

x[0] := Vector(2, {(1) = -2, (2) = -2});

r[0] := b-A*x[0];

k := 0;

while r[k] <> 0

do k := k+1;

a[k] := Transpose(r[k-1])*r[k-1]/(Transpose(r[k-1])*A*r[k-1]);

x[k] := x[k-1]+a[k]*r[k-1];

r[k] := b-A*x[k]

end do; x := x[k]; print(x) end proc

So I use a matrix A and a vector B to test with the initial guess of x(0) as (-2,-2) and it just continues evaluating for 5-10 min and eventually the computer stalls and ends maple.

Any ideas about what I'm doing wrong?

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