Adaptive Cubic Regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization

stefania Bellavia (stefania.bellaviaunifi.it)
Gianmarco Gurioli (gianmarco.gurioliunifi.it)
Benedetta Morini (benedetta.moriniunifi.it)

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 largescale finite-sum minimization based on subsampled Hessian is discussed and analyzed in both a deterministic andmprobabilistic manner and equipped with numerical experiments on synthetic and real datasets.

Keywords: Adaptive regularization with cubics; nonconvex optimization; worst-case analysis, finite-sum optimization.

Category 1: Nonlinear Optimization (Unconstrained Optimization )

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Entry Submitted: 08/19/2018
Entry Accepted: 08/19/2018
Entry Last Modified: 12/09/2019

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