Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence Analysis of Gradient Algorithms on Riemannian Manifolds
  Without Curvature Constraints and Application to Riemannian Mass   We study the convergence issue for the gradient algorithm (employing general
step sizes) for optimization problems on general Riemannian manifolds (without
curvature constraints). Under the assumption of the local
convexity/quasi-convexity (resp. weak sharp minima), local/global convergence
(resp. linear convergence) results are established. As an application, the
linear convergence properties of the gradient algorithm employing the constant
step sizes and the Armijo step sizes for finding the Riemannian $L^p$
($p\in[1,+\infty)$) centers of mass are explored, respectively, which in
particular extend and/or improve the corresponding results in
\cite{Afsari2013}.

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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin