I'm not sure how to show this:
$proj_x(conv(S)) = conv(proj_x(S))$ where S $\in R^{n+p}$
2026-03-25 04:58:46.1774414726
Prove projection of convex hull = convex hull of projection
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Start with a point in the projection of $conv(S)$ and, using the definition of convex hull, show it is in convex hull of the projection of $S$. Then take a point in the convex hull of the projection of $S$ and, again using the definition of convex hull, show it is in the projection of $conv(S)$.