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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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psd condition for matrix completion

The nuclear norm minimization for the matrix completion problem is given by \begin{align} \textrm{minimize } \quad &\|X\|_{*}\\ \textrm{subject to } \quad & X_{ij}=M_{ij} \quad \forall (i,j)\in \Om …