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So you're going to always only do numerical computations only? Good luck solving even simple optimization problems that have a few parameters.
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I believe finite differences are no less general than derivatives.

Well, the belief is not worth much here. How do you express optimality condition of the form f'(x) = 0 with finite difference? Answer: you don't.

But if this doesn't ring a bell, it's probably better to drop this.




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