Examples of slow convergence for adaptive regularization optimization
methods are not isolated
Examples of slow convergence for adaptive regularization optimization
methods are not isolated
The adaptive regularization algorithm for unconstrained nonconvex optimization was shown in Nesterov and Polyak (2006) and Cartis, Gould and Toint (2011) to require, under standard assumptions, at most $\mathcal{O}(\epsilon^{3/(3-q)})$ evaluations of the objective function and its derivatives of degrees one and two to produce an $\epsilon$-approximate critical point of order …