minimum of a function

Hello sir;

i am trying to find minimum of a function by putting more than one vectors in a single step to get a constant cost value.

 bk=magic(4)=[16     2     3    13
              5    11    10     8
              9     7     6    12
              4    14    15     1]

 function=bk1'*H1'*H1*bk1-2*yr'*H1*bk1;

where yr is a column vector, H1 is a square matrix and bk1 is a column of bk.

i want to put each vector of bk in above function and select the minimum value in a single command.

i tried this one but it doesn't works.

[cost_value, indx]=min(abs(bk(:,[1:end])'*H1'*H1*bk(:,[1:end])-2*yr'*H1*bk(:,[1:end])));

please help

[John D'Errico]

As you wrote it, that is not a function. It is an expression. Also, you cannot use the name "function" for a variable name.

If you are trying to find a minimum of a function, use an optimizer. Min is not an optimizer. Tools like fminsearch, fminunc, fmincon are optimzers.

[Arif Ullah khan]

thnx for reply how but can i implement this to get the minimum value as well the index of the vector which gives the minimun value

[Arif Ullah khan]

actually i want to find the column of bk which gives minimum value for the expression

Answer 1

[Image Analyst]

What is bk1 and H?

Anyway, why not just assign it to a numerical array and use min:

f =bk1'*H1'*H1*bk1-2*yr'*H1*bk1
[minFValue, linearIndexAtMinFValue] = min(f(:));

or

[rowAtMin, colAtMin] = find(f == min(f(:)))

[Arif Ullah khan]

bk1 is each column of bk matrix while H1 is a square matrix actually i want to find the column of bk which gives minimum value for the expression

[Image Analyst]

Yep, my code will do it.