Hello, I'm planning to use this function to optimize a least squares objective. I noticed that the "norm" argument defaults to "inf" or max norm. Does this mean that (by default) the search is done in max-norm space rather than L2/Euclidean norm space? Should I be worried about this setting? Thanks, Jason -- Jason Rennie Research Scientist, ITA Software http://www.itasoftware.com/
On 20-May-09, at 3:51 PM, Jason Rennie wrote:
Hello,
I'm planning to use this function to optimize a least squares objective. I noticed that the "norm" argument defaults to "inf" or max norm. Does this mean that (by default) the search is done in max-norm space rather than L2/Euclidean norm space? Should I be worried about this setting?
No; the termination criterion is based on the norm of the gradient. By default, it uses the infinity norm. This simply means that by default, the search terminates when _every_ element of the returned gradient is less than gtol. This is a bit easier to think about than figuring out a tolerance on the 2-norm of the gradient vector, especially in very high dimensional spaces. David
Makes sense. Thanks! Jason On Wed, May 20, 2009 at 4:48 PM, David Warde-Farley <dwf@cs.toronto.edu>wrote:
On 20-May-09, at 3:51 PM, Jason Rennie wrote:
Hello,
I'm planning to use this function to optimize a least squares objective. I noticed that the "norm" argument defaults to "inf" or max norm. Does this mean that (by default) the search is done in max-norm space rather than L2/Euclidean norm space? Should I be worried about this setting?
No; the termination criterion is based on the norm of the gradient. By default, it uses the infinity norm.
This simply means that by default, the search terminates when _every_ element of the returned gradient is less than gtol. This is a bit easier to think about than figuring out a tolerance on the 2-norm of the gradient vector, especially in very high dimensional spaces.
David _______________________________________________ SciPy-user mailing list SciPy-user@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-user
-- Jason Rennie Research Scientist, ITA Software http://www.itasoftware.com/
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