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Aug 5, 2011 at 1:02 comment added user16953 I agree with the counter example. It shows that the statement is not true for the usual norm. But if the norm (and the associated projection) is appropriatly constructed from the form of the objective than maybe (0,0) ca give us information on the minimizer on S. This means that my question was not properly written. Many thanks for your feedback.
Aug 4, 2011 at 19:27 history answered Robert Israel CC BY-SA 3.0