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First Order Methods for Optimization on Riemannian Manifolds

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Abstract

This chapter considers optimization problems on Riemannian manifolds and presents asymptotic and iteration-complexity analysis for gradient and subgradient methods on manifolds with sectional curvatures bounded from below. It also establishes asymptotic and iteration-complexity analysis for the proximal point method on Hadamard manifolds.

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Acknowledgements

This work was supported by CNPq 302473∕2017 − 3, 408151∕2016 − 1 and 424860∕2018 − 0, FAPEG/CNPq/PPP—03/2015 and FAPEG/PRONEM—201710267000532. This work is part of a measure which is co-financed by tax revenue based on the budget approved by the members of the Saxon state parliament. Financial support is gratefully acknowledged.

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Authors and Affiliations

  1. Universidade Federal de Goiás, Institute of Mathematics Statistics, Goiânia, GO, Brazil

    Orizon P. Ferreira & Leandro F. Prudente

  2. TU Chemnitz, Fakultät für Mathematik, Chemnitz, Germany

    Maurício S. Louzeiro

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  1. Orizon P. Ferreira
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  2. Maurício S. Louzeiro
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Correspondence to Orizon P. Ferreira .

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  1. Faculty of Mathematics, University of Vienna, Wien, Austria

    Philipp Grohs

  2. Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Martin Holler

  3. Department of Mathematics and Natural Sciences, Hochschule Darmstadt, Darmstadt, Germany

    Andreas Weinmann

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Ferreira, O.P., Louzeiro, M.S., Prudente, L.F. (2020). First Order Methods for Optimization on Riemannian Manifolds. In: Grohs, P., Holler, M., Weinmann, A. (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, Cham. https://doi.org/10.1007/978-3-030-31351-7_18

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