On Global Rates for Regularization Methods based on Secant Derivative Approximations
An inexact framework for high-order adaptive regularization methods is presented, in which approximations may be used for the $p$th-order tensor, based on lower-order derivatives. Between each recalculation of the $p$th-order derivative approximation, a high-order secant equation can be used to update the $p$th-order tensor as proposed in (Welzel 2024) or the approximation can be kept constant in a lazy manner. When refreshing the $p$th-order tensor approximation after $m$ steps, an exact evalu…
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