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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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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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Matt J

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