User menu

Low-rank retractions: a survey and new results

Bibliographic reference Absil, Pierre-Antoine ; Oseledets, Ivan V.. Low-rank retractions: a survey and new results. In: Computational Optimization and Applications : an international journal, Vol. 62, no. 1, p. 5-29 (September 2015)
Permanent URL
  1. Absil P.-A., Amodei Luca, Meyer Gilles, Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries, 10.1007/s00180-013-0441-6
  2. Absil P.-A., Baker C.G., Gallivan K.A., Trust-Region Methods on Riemannian Manifolds, 10.1007/s10208-005-0179-9
  3. Adler R. L., Newton's method on Riemannian manifolds and a geometric model for the human spine, 10.1093/imanum/22.3.359
  4. Absil P.-A., Malick Jérôme, Projection-like Retractions on Matrix Manifolds, 10.1137/100802529
  5. Absil, P.-A., Mahony, R., Sepulchre. R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, NJ (2008).
  6. Boumal, N., Mishra, B., Absil, P.-A., Sepulchre, R.: Manopt, a matlab toolbox for optimization on manifolds. J. Mach. Learn. Res. 15, 1455–1459 (2014).
  7. Boothby, W.M.: An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised Second Edition. Academic Press, London (2003)
  8. Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences, 3rd edn. Johns Hopkins University Press, Baltimore, MD (1996)
  9. Koch Othmar, Lubich Christian, Dynamical Low‐Rank Approximation, 10.1137/050639703
  10. Kressner Daniel, Steinlechner Michael, Vandereycken Bart, Low-rank tensor completion by Riemannian optimization, 10.1007/s10543-013-0455-z
  11. Lee, J.M.: Introduction to Smooth Manifolds, Volume 218 of Graduate Texts in Mathematics. Springer, New York (2003)
  12. Lubich, C., Oseledets, I.V.: A projector-splitting integrator for dynamical low-rank approximation (2013) arXiv:1301.1058v2
  13. Luenberger David G., The Gradient Projection Method Along Geodesics, 10.1287/mnsc.18.11.620
  14. Mishra B., Meyer G., Bach F., Sepulchre R., Low-Rank Optimization with Trace Norm Penalty, 10.1137/110859646
  15. Mishra, B., Meyer, G., Bonnabel, S., Sepulchre, R.: Fixed-rank matrix factorizations and Riemannian low-rank optimization (2013). arXiv:1209.0430v2
  16. Mishra, B., Sepulchre, R.: R3MC: a Riemannian three-factor algorithm for low-rank matrix completion, 2014. Accepted for publication in the proceedings of the 53rd IEEE Conference on Decision and Control (2014). arXiv:1306.2672v2
  17. Rosen J. B., The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints, 10.1137/0109044
  18. Ring Wolfgang, Wirth Benedikt, Optimization Methods on Riemannian Manifolds and Their Application to Shape Space, 10.1137/11082885x
  19. Shub, M.: Some remarks on dynamical systems and numerical analysis. In L. Lara-Carrero and J. Lewowicz, (eds), Proceedings of the VII ELAM. Equinoccio, U. Simón Bolívar, Caracas, pp. 69–92 (1986)
  20. Shalit, U., Weinshall, D., Chechik, G.: Online learning in the embedded manifold of low-rank matrices. J. Mach. Learn. Res. 13, 429–458 (2013)
  21. Vandereycken Bart, Low-Rank Matrix Completion by Riemannian Optimization, 10.1137/110845768