### 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 $$\geq$$.