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Thread Subject:
How does TolX work?

Subject: How does TolX work?

From: Apon Mohaimen

Date: 8 Dec, 2010 10:53:04

Message: 1 of 3

Hi,
I was just wondering how the tolerance criteria defined by Tolx works when x is a vector of parameters. Does the optimization iteration stop when for any one of the elements in x the criteria is met?

Thanks
Apon

Subject: How does TolX work?

From: Ahmed Fasih

Date: 8 Dec, 2010 12:26:05

Message: 2 of 3

> I was just wondering how the tolerance criteria defined by Tolx works when x is a vector of parameters. Does the optimization iteration stop when for any one of the elements in x the criteria is met?

"Tolerances and Stopping Criteria" http://www.mathworks.com/help/toolbox/optim/ug/f12471.html#brhv4_o-1

"TolX is a lower bound on the size of a step, meaning the norm of (xi – xi+1). If the solver attempts to take a step that is smaller than TolX, the iterations end."

Therefore, it is not an element-wise tolerance, but a full vector norm, presumably the 2-norm, sqrt((xold - xnew)' * (xold-xnew)).

Subject: How does TolX work?

From: Apon Mohaimen

Date: 8 Dec, 2010 14:13:05

Message: 3 of 3

Thanks a lot.

"Ahmed Fasih" <fasih.1NOSPAM@osu.edu.nospam> wrote in message <idntgs$i51$1@fred.mathworks.com>...
> > I was just wondering how the tolerance criteria defined by Tolx works when x is a vector of parameters. Does the optimization iteration stop when for any one of the elements in x the criteria is met?
>
> "Tolerances and Stopping Criteria" http://www.mathworks.com/help/toolbox/optim/ug/f12471.html#brhv4_o-1
>
> "TolX is a lower bound on the size of a step, meaning the norm of (xi – xi+1). If the solver attempts to take a step that is smaller than TolX, the iterations end."
>
> Therefore, it is not an element-wise tolerance, but a full vector norm, presumably the 2-norm, sqrt((xold - xnew)' * (xold-xnew)).

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