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I have a loss function: $$L(\beta)=\frac{1}{2}\sum_{i=1}^n (y_i -x_i^\top\beta)^2+\frac{\lambda}{2}\|\beta\|_{2}^2$$

I calculated: $$\nabla L(\beta) = X^T (X \beta - y)+ \lambda \beta$$ $$\nabla^2 L(\beta) = X^T X + \lambda I$$

Now I have to find conditions under which loss function is strongly-convex. How can I do that?

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1 Answers1

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Solved it. when $\lambda > 0$ and when X (mxn) full rank and $m \geq n$

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