Re: Linear Optimization problem............

madsvlad@xxxxxxxxx wrote:
> Thanks for the help. Your explanation was extremely helpful.
> The whole thing makes much more sense to me now. I have one
> further question related to the actual minimization process:
>> Then sum_i^N di^2 = (y-z)'*(y-z) + (y-z)'*X*t + t'*X'*X*t,
>> which can be minimized with respect to t in the usual way.
>
> I'm assuming this means that I need to minimize the gradient
> of the distance function?

It's probably better to say that you need to minimize the norm
of the gradient than it is to say that you need to minimize the
gradient itself. Or, better yet, just say that you need to set
the gradient to zero.

>
> grad(di^2) = -2X'*X*t - 2X*(y-z)
>
> Minimization occurs when the gradient is zero hence:
>
> X'*X*t + X'*(y-z) = 0
>
> Is this correct?

Yes, except you've used the formula from my initial post,
which was wrong. The correct expression for sum(di^2) is
(y-z)'*(y-z) - 2(y-z)'*X*t + t'*X'*X*t,
its gradient is -2X'*(y-z) + 2X'*X*t,
and the equation to be solved is X'*X*t = X'*y.

.

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