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for questions involving inequalities, upper and lower bounds.

3 votes

Convexity and Lipschitz continuity

A partial answer: if you're willing to strengthen your assumption and suppose $f\in C^2(\mathbb{R}^n)$, then yes. Otherwise, I'm not sure. Functions that satisfy - $$\langle\nabla f(x)-\nabla f(y),x- …
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