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In this paper, we generalize (accelerated) Newton's method with cubicregularization under inexact second-order information for (strongly) convexoptimization problems. Under mild assumptions, we provide global rate ofconvergence of these methods and show the explicit dependence of the rate ofconvergence on the problem parameters. While the complexity bounds of ourpresented algorithms are theoretically worse than those of their exactcounterparts, they are at least as good as those of the optimal first-ordermethods. Our numerical experiments also show that using inexact Hessians cansignificantly speed up the algorithms in practice.

Second-Order Methods with Cubic Regularization Under Inexact Information