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Mock exam 2015 multiple-output regression

Hello,
For the question (B) it is asked to discuss the conditions under which the minimum is unique. I agree that the equation always have a solution because the matrix is always invertible. However, for the minimum to be UNIQUE don't we have the condition that the objective is convex?
Thank you for your answer.
Screenshot 2022-01-15 at 09.08.54.jpgScreenshot 2022-01-15 at 09.09.14.jpg

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Hi,

The objective function L is, by design, a convex function. There are no conditions (on the unknown parameters ) that need to be set.
Note that one can derive Eq. 10. (which describes a unique solution) without setting any further conditions.

Karim

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