Adaptive Cubic Regularization Methods with Dynamic Inexact Hessian Information and Applications to Finite-Sum Minimization
Optimization and Control
2019-12-04 v3 Numerical Analysis
Numerical Analysis
Abstract
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 subsampled Hessian is discussed and analyzed in both a deterministic and probabilistic manner and equipped with numerical experiments on synthetic and real datasets.
Cite
@article{arxiv.1808.06239,
title = {Adaptive Cubic Regularization Methods with Dynamic Inexact Hessian Information and Applications to Finite-Sum Minimization},
author = {Stefania Bellavia and Gianmarco Gurioli and Benedetta Morini},
journal= {arXiv preprint arXiv:1808.06239},
year = {2019}
}