A Broyden Class of Quasi-Newton Methods for Riemannian Optimization

Authors

Wen Huang, K. A. Gallivan, P.-A. Absil

Abstract

This paper develops and analyzes a generalization of the Broyden class of quasi-Newton methods to the problem of minimizing a smooth objective function f on a Riemannian manifold. A condition on vector transport and retraction that guarantees convergence and facilitates efficient computation is derived. Experimental evidence is presented demonstrating the value of the extension to the Riemannian Broyden class through superior performance for some problems compared to existing Riemannian BFGS methods, in particular those that depend on differentiated retraction.

Key words

Riemannian optimization; manifold optimization; Quasi-Newton methods; Broyden methods; Stiefel manifold;

Status

SIAM Journal on Optimization, 25:3, pp. 1660-1685, 2015.

Download

Technical report: PDF
Local Copy of SIOPT version: PDF
Experiment code: matlab zip or ROPTLIB (ROPTLIB is recommanded)

BibTex entry

Technical Report
@TECHREPORT{HuaGalAbs2015,
author = "Wen Huang and K. A. Gallivan and P.-A. Absil",
title = "A Broyden class of quasi-Newton methods for Riemannian optimization",
institution = "U.C.Louvain",
year = 2015,
number = "UCL-INMA-2014.01",
}

SIOPT
@article{HuaGalAbs2015,
author = {Wen Huang and K. A. Gallivan and P.-A. Absil},
title = {A Broyden Class of Quasi-Newton Methods for Riemannian Optimization},
journal = {SIAM Journal on Optimization},
volume = {25},
number = {3},
pages = {1660-1685},
year = {2015},
doi = {10.1137/140955483},
}