A Scaled Gradient Projection Method for Minimization over the Stiefel Manifold

Harry Oviedo, Oscar Dalmau

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

In this paper we consider a class of iterative gradient projection methods for solving optimization problems with orthogonality constraints. The proposed method can be seen as a forward-backward gradient projection method which is an extension of a gradient method based on the Cayley transform. The proposal incorporates a self-adaptive scaling matrix and the Barzilai-Borwein step-sizes that accelerate the convergence of the method. In order to preserve feasibility, we adopt a projection operator based on the QR factorization. We demonstrate the efficiency of our procedure in several test problems including eigenvalue computations and sparse principal component analysis. Numerical comparisons show that our proposal is effective for solving these kind of problems and presents competitive results compared with some state-of-art methods.

Original languageEnglish
Title of host publicationAdvances in Soft Computing - 18th Mexican International Conference on Artificial Intelligence, MICAI 2019, Proceedings
EditorsLourdes Martínez-Villaseñor, Ildar Batyrshin, Antonio Marín-Hernández
PublisherSpringer
Pages239-250
Number of pages12
ISBN (Print)9783030337483
DOIs
StatePublished - 2019
Externally publishedYes
Event18th Mexican International Conference on Artificial Intelligence, MICAI 2019 - Xalapa, Mexico
Duration: 27 Oct 20192 Nov 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11835 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th Mexican International Conference on Artificial Intelligence, MICAI 2019
Country/TerritoryMexico
CityXalapa
Period27/10/192/11/19

Keywords

  • Gradient projection method
  • Nonlinear programming
  • Orthogonality constraints
  • Stiefel manifold

Fingerprint

Dive into the research topics of 'A Scaled Gradient Projection Method for Minimization over the Stiefel Manifold'. Together they form a unique fingerprint.

Cite this