## Convergence of gradient descent in one variable

What are the sufficient conditions for gradient descent to converge in one variable?

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 This seems much too vague. Do you want answers in the direction "Constant step-size work for these functions" or the other way round (e.g. "for convex functions this step-sizes work"). If you use "exact step-sizes", then obviously gradient descent will work for any function with one global minimum. – Dirk Oct 13 at 19:07