Question exam 2019

Hello,

I have troubles understanding the logic of the correction of question 23 in exam 2019: we have that

\( y^* is an optimum \Leftrightarrow \nabla g(y^*)^T (y - y^*) >0 \)

So we verify if the RHS is verified for the proposed \( y^* \) in order to conclude the LHS: what I don't understand is that we check that

\( \nabla g(y^*)^T (y - y^*) \textbf{=}0 \) which is not equivalent to \( \nabla g(y^*)^T (y - y^*) >0 \)

Thanks in advance for any help!

Best,

Yann

Top comment

The optimality condition should have been \(\geq\) instead of \(>\) (according to Lemma 1.27 of the lecture notes). Looks like a typo. Proving equality also proves \(\geq\).

I was also very confused by this. It seems to me that they are doing some sort of proof by induction, but it doesn't convince me.

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Top comment

The optimality condition should have been \(\geq\) instead of \(>\) (according to Lemma 1.27 of the lecture notes). Looks like a typo. Proving equality also proves \(\geq\).

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