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

Autor: Gianmarco Gurioli, Stefania Bellavia, Benedetta Morini

Publikováno v: IMA Journal of Numerical Analysis. 41:764-799

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. T

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab4547a8a7a16243340225b642048f55
https://doi.org/10.1093/imanum/drz076

Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg–de Vries equation

Autor: Luigi Brugnano, Yajuan Sun, Gianmarco Gurioli

Publikováno v: Journal of Computational and Applied Mathematics. 351:117-135

In this paper we study the efficient solution of the well-known Korteweg–de Vries equation, equipped with periodic boundary conditions. A Fourier–Galerkin space semi-discretization at first provides a large-size Hamiltonian ODE problem, whose sol

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https://doi.org/10.1016/j.cam.2018.10.014

Spectrally accurate energy‐preserving methods for the numerical solution of the 'good' Boussinesq equation

Autor: Chengjian Zhang, Gianmarco Gurioli, Luigi Brugnano

Publikováno v: Numerical Methods for Partial Differential Equations. 35:1343-1362

In this paper we study the geometric solution of the so called "good" Boussinesq equation. This goal is achieved by using a convenient space semi-discretization, able to preserve the corresponding Hamiltonian structure, then using energy-conserving R

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https://doi.org/10.1002/num.22353

Stochastic Analysis of an Adaptive Cubic Regularisation Method under Inexact Gradient Evaluations and Dynamic Hessian Accuracy

Autor: Gianmarco Gurioli, Stefania Bellavia

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still considered, th

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Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

Autor: Ph. L. Toint, Gianmarco Gurioli, Stefania Bellavia, Benedetta Morini

Publikováno v: Bellavia, S, Gurioli, G, Morini, B & Toint, P 2020, ' Adaptive regularization algorithms with inexact evaluations for nonconvex optimization ', SIAM Journal on Optimization, vol. 29, no. 4, pp. 2881-2915 . https://doi.org/10.1137/18M1226282

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constrai

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