Simpler flag optimization Article Swipe
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Flag (linear algebra)
Hessian matrix
Tangent vector
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Mathematical analysis
Pure mathematics
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Zehua Lai
,
Lek‐Heng Lim
,
Ke Ye
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.00212
· OA: W4310629065
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.00212
· OA: W4310629065
We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel transport, gradient, Hessian, etc -- have closed-form analytic expressions that are computable with standard numerical linear algebra. Furthermore, we are able to derive a coordinate descent method in the flag manifold that performs well compared to other gradient descent methods.
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