Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured Quasi-Newton Methods for Optimization with Orthogonality
  Constraints   In this paper, we study structured quasi-Newton methods for optimization
problems with orthogonality constraints. Note that the Riemannian Hessian of
the objective function requires both the Euclidean Hessian and the Euclidean
gradient. In particular, we are interested in applications that the Euclidean
Hessian itself consists of a computational cheap part and a significantly
expensive part. Our basic idea is to keep these parts of lower computational
costs but substitute those parts of higher computational costs by the
limited-memory quasi-Newton update. More specically, the part related to
Euclidean gradient and the cheaper parts in the Euclidean Hessian are
preserved. The initial quasi-Newton matrix is further constructed from a
limited-memory Nystr\"om approximation to the expensive part. Consequently, our
subproblems approximate the original objective function in the Euclidean space
and preserve the orthogonality constraints without performing the so-called
vector transports. When the subproblems are solved to sufficient accuracy, both
global and local q-superlinear convergence can be established under mild
conditions. Preliminary numerical experiments on the linear eigenvalue problem
and the electronic structure calculation show the effectiveness of our method
compared with the state-of-art algorithms.

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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph