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Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

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Solution to a Strongly Convex Non-smooth Minimization Problem involving an L1 Norm

Let $X \in \mathbb{R}^{n \times d}, w \in \mathbb{R}^d, y \in \{\pm 1\}^{n}, \alpha \in [0,1], \lambda \in \mathbb{R}$. I have an expression that looks as follows $\frac{1}{2}\|Xw -y \|_{2}^2 + \alph …
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