Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 25, Issue 3, Pages 1660-1685Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140955483
Keywords
Riemannian optimization; manifold optimization; quasi-Newton methods; Broyden methods; Stiefel manifold
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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.
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