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## Mock 2018 QCM Regularization term

Hello,

Can you give me an example of an objective where we had a regularization term in order to render the minimization problem strictly convex/concave? :/ I am not convinced.

Thank you for your help!

Take linear regression for example, the hessian is given by \(XX^\top /N\) for \(X\in \mathcal{R}^{d\times N}\).

If this matrix is not full rank then the problem is not strictly convex and in particular we can't invert the matrix \(XX^\top\), but with ridge regression we add a \(\lambda\) to all directions and thus ensure that the smallest eigenvalue of the hessian is at least this \(\lambda\), thus we have made the problem strictly convex.

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