On Fri, Dec 21, 2012 at 11:29 AM, Feiveson, Alan H. (JSC-SK311)
<alan.h.feiveson@nasa.gov> wrote:
> You can't optimize a function of median |ei| by setting it's derivative to zero because the partial derivatives don't exist at ei = 0. You would have do something like linear programming (as is done in LAD regression).
>
True but you can do some nifty approximations, which is how interior
point/barrier methods work, by approximating the L1 distance function
with a sequence of functions that are smooth but grow arbitrarily
close to L1.
http://en.wikipedia.org/wiki/Interior_point_method
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