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.

Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization / Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - STAMPA. - 41:(2021), pp. 764-799. [10.1093/imanum/drz076]

Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization

Stefania Bellavia;Gianmarco Gurioli;Benedetta Morini
2021

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.
2021
41
764
799
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1182764
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