Text

On High-Order Multilevel Optimization Strategies

We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on $q$th-order Taylor models (with $q\geq 1$) that have been recently proposed in the literature. The use of high-order models, while decreasing the worst-case complexity bound, makes these methods computationally more expensive. Hence, to counteract this effect, we propose a multilevel strategy that exploits a hierarchy of problems of decreasing dimension, still approximating the original one, to reduce the global cost of the step computation. A theoretical analysis of the family of methods is proposed. Specifically, local and global convergence results are proved, and a worst-case complexity bound to reach first-order stationary points is also derived. A multilevel version of the well-known adaptive regularization by cubics (corresponding to $q=2$ in our setting) has been implemented, as well as a multilevel third-order method ($q=3$). Numerical experiments clearly highlight the relevance of the new multilevel approaches leading to considerable computational savings compared to their one-level counterparts.


Read More: https://epubs.siam.org/doi/abs/10.1137/19M1255355

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.1 January-March 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 307 - 330

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ERROR BOUND
NONLINEAR OPTIMIZATION
TENSOR METHODS
MULTILEVEL METHODS
HIGH-ORDER OPTIMIZATION MODEL
COMPLEXITY ESTIMATION

Info Detail Spesifik

-

Pernyataan Tanggungjawab

Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur

Versi lain/terkait

Lampiran Berkas

Komentar