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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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Echange of Infimum Integral with Pointwise Infimum

If $U$ is non-empty then the value of either side is $m \mu(\mathcal{X})$ where $m= \inf \{y^2 ~|~ g(y)<M\}$. If $\mu$ is non-finite then $m=0$. To see this note first that for $f_1,f_2 \in U$ the f …
Martin Kell's user avatar