I have a convex function on open interval. We know, that there is no more than one minima, but how do we prove, that there is at least one?
2026-04-05 23:05:32.1775430332
Minima of convex function
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This is not always guaranteed. Consider the function $f : (0,1) \to \mathbb{R}$ by $f(x) = x$. Since $f$ is linear, it is also convex. On the other hand, it has no minimum.