3 years ago

Theoretical study of an adaptive cubic regularization method with dynamic inexact Hessian information.

Gianmarco Gurioli, Benedetta Morini, Stefania Bellavia

We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure is given. The key property of ARC framework, constituted by optimal worst-case function/derivative evaluation bounds for first- and second-order critical point, is guaranteed. Application to large-scale finite-sum minimization based on sub-sampled Hessian is discussed and analyzed in both a deterministic and probabilistic manner.

Publisher URL: http://arxiv.org/abs/1808.06239

DOI: arXiv:1808.06239v1

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