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Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds

We extend coordinate descent to manifold domains and provide convergence analyses for geodesically convex and nonconvex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of TSD is the appropriate choice of subspace at each iteration. To this end, we propose two novel conditions, the (C, r)-norm and C-randomized norm conditions on deterministic and randomized modes of subspace selection, respectively, that promise convergence for smooth functions and that are satisfied in practical contexts. We propose two subspace selection rules, one deterministic and another randomized, of particular practical interest on the Stiefel manifold. Our proof-of-concept numerical experiments on the sparse principal component analysis problem demonstrate TSD’s efficacy.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.48 No.1 February 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 127-159

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

COORDINATE DESCENT
FIRST-ORDER METHODS
OPTIMIZATION ON MANIFOLDS

Info Detail Spesifik

https://doi.org/10.1287/moor.2022.1253

Pernyataan Tanggungjawab

David H. Gutman, Nam Ho-Nguyen

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