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Let f(x) be strongly-convex. Can its minimizer be unbounded? I suspect not. Can we obtain a bound on it in relation to the strong-convexity constant?

I believe an equivalent formulation of this question is: Is the minimizer, $x^\star$, of a strongly-convex function, $f(x)$, in a compact or bounded subset of $\mathbb{R}^n$?

Thank you!

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