[SciPy-user] argmin and optimization
Alan G Isaac
aisaac@american....
Thu Jul 26 07:18:53 CDT 2007
On Thu, 26 Jul 2007, Nils Wagner apparently wrote:
> I would like to implement an algorithm described by Golub and Liao.
> Get the source from here: http://citeseer.ist.psu.edu/638954.html
> The central question is the following. How do I implement the operator
> P_\Omega(\cdot) in scipy ?
> The definition is as follows (\LaTex notation)
> P_\Omega(y) = \textrm{argmin}\limits_{x \in \Omega} \|x-y\|_2 \forall \,
> y \in \mathds{R}^n
> \Omega = \{ x \in \mathds{R}^n | <x,x> \le 1 \}.
It looks like you are saying:
get as close to y as possible without leaving the unit
sphere. Is that right? This is just y if y is in the
unit sphere and it is y normalized to unit length if
y is outside the unit sphere.
Please post the code when you finish the algorithm.
Cheers,
Alan Isaac
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