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Dayu

What is the precise definition of tolX in optimization toolbox

Asked by Dayu
on 19 Jul 2013

What is the precise definition of tolX in optimization toolbox? The manual uses a vague term "tolerance". More specifically, when X is a vector, is it defined as the l2 norm of X or l-infinity norm of X? This makes a huge difference when dealing with a large vector.

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1 Answer

Matt J
Answer by Matt J
on 19 Jul 2013
Edited by Matt J
on 19 Jul 2013

According to,

http://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html

TolX isn't even always an absolute bound on a norm:

"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. TolX is sometimes used as a relative bound, meaning iterations end when (xi – xi+1) < TolX*(1 + xi), or a similar relative measure."

However, presumably the norm referred to in the above excerpt is the l2 norm, since it does not say otherwise.

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