# Time bound for gradient descent

Have you seen any analytic bound on gradient descent (for number of iterations to achieve to $\epsilon$ error, and possibly based on the form of cost function and initial value)?

Here is the problem; I have a cost function which is being optimized by gradient descent. Someone has changed the cost function, in some ways, and has shown to converge to the main result (the result of gradient descent on the main cost function). I want to compare the convergence-time bounds for these two algorithm ...

Are you aware of any such bounds for similar optimization algorithms ?

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