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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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Current state of the Komlos conjecture on vector balancing

For fixed $d$, one can actually achieve a bound independent of $n$. More precisely, $K=K(d)=O(\sqrt{d})$ is fine, uniformly in $n$. Proof : the unit ball of $\mathbb{R}^d$ can be covered by $2C^d$ ba …
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