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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.
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Matrix inequality $a X \succeq arcsin(X)$ for some $a > 0$
Let $X \in S^{n}_{+}$ be a positive semi-definite matrix with $X_{ii} = 1$ for all $i \leq n$ (thus $X$ is a correlation matrix).
Since $X$ is positive semi-definite, we have $|X_{ij}| \leq 1$ for any …