Adaptative cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems with a shifted Hessian in the spirit of the modified Newton method. In the simplest case, the shift is a multiple of the identity, which is typically identified by trial and error. We propose a scalable implementation of ARC in which we solve a set of shifted systems concurrently by way of an appropriate Krylov solver.
Published October 2015 , 13 pages
G15109.pdf (400 KB)