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Inexact Nonconvex Newton-Type Methods

For solving large-scale nonconvex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to inexact subproblem solves, both the gradient and Hessian are suitably estimated. Using certain conditions on such approximations, we show that our proposed inexact methods achieve similar optimal worst-case iteration complexities as the exact counterparts. In the context of finite-sum problems, we then explore randomized subsampling methods as ways to construct the gradient and Hessian approximations and examine the empirical performance of our algorithms on some model problems. We empirically demonstrate that our proposed algorithms are practically implementable in that failure to precisely fine-tune the associated hyperparameters is unlikely to result in unwanted behaviors, for example, divergence or stagnation.

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Informasi Detail

Judul Seri

INFORMS JOURNAL ON OPTIMIZATION; Vol.3 No.2 Spring 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 154 - 182

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

NONCONVEX OPTIMIZATION
TRUST REGION
INEXACT GRADIENT
CUBIC REGULARIZATION
INEXACT HAZZIEN

Info Detail Spesifik

https://doi.org/10.1287/ijoo.2019.0043

Pernyataan Tanggungjawab

Zhewei Yao, Peng Xu, Fred Roosta, Michael W. Mahoney

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