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On the Riemannian geometry defined by self-concordant barriers and interior-point methods

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  • NESTEROV , Yu.
  • TODD, Mike

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  • NESTEROV , Yu. & TODD, Mike, 2002. "On the Riemannian geometry defined by self-concordant barriers and interior-point methods," LIDAM Reprints CORE 1595, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1595
    DOI: 10.1007/s102080010032
    Note: In : Foundations of Computational Mathematics, 2, 333-361, 2002
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    Cited by:

    1. J. X. Cruz Neto & O. P. Ferreira & P. R. Oliveira & R. C. M. Silva, 2008. "Central Paths in Semidefinite Programming, Generalized Proximal-Point Method and Cauchy Trajectories in Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 227-242, November.
    2. Glaydston C. Bento & Orizon P. Ferreira & Jefferson G. Melo, 2017. "Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 548-562, May.
    3. E. A. Papa Quiroz & P. R. Oliveira, 2007. "New Self-Concordant Barrier for the Hypercube," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 475-490, December.
    4. João S. Andrade & Jurandir de O. Lopes & João Carlos de O. Souza, 2023. "An inertial proximal point method for difference of maximal monotone vector fields in Hadamard manifolds," Journal of Global Optimization, Springer, vol. 85(4), pages 941-968, April.
    5. T. Bittencourt & O. P. Ferreira, 2017. "Kantorovich’s theorem on Newton’s method under majorant condition in Riemannian manifolds," Journal of Global Optimization, Springer, vol. 68(2), pages 387-411, June.
    6. Jean-Baptiste Hiriart-Urruty & Jérôme Malick, 2012. "A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 551-577, June.
    7. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    8. Maxim Raginsky & Angelia Nedić, 2016. "Online Discrete Optimization in Social Networks in the Presence of Knightian Uncertainty," Operations Research, INFORMS, vol. 64(3), pages 662-679, June.
    9. Patrick M Wensing & Jean-Jacques Slotine, 2020. "Beyond convexity—Contraction and global convergence of gradient descent," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-29, August.
    10. NESTEROV, Yurii & NEMIROVSKI, Arkadi, 2003. "Central path and Riemannian distances," LIDAM Discussion Papers CORE 2003051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Orizon P. Ferreira & Mauricio S. Louzeiro & Leandro F. Prudente, 2020. "Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 507-533, February.
    12. Gregório, R.M. & Oliveira, P.R. & Alves, C.D.S., 2019. "A two-phase-like proximal point algorithm in domains of positivity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 67-89.
    13. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.
    14. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos Oliveira Souza, 2019. "Computing Riemannian Center of Mass on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 977-992, December.
    15. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
    16. Teles A. Fernandes & Orizon P. Ferreira & Jinyun Yuan, 2017. "On the Superlinear Convergence of Newton’s Method on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 828-843, June.
    17. Edvaldo E. A. Batista & Glaydston de Carvalho Bento & Orizon P. Ferreira, 2016. "Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 916-931, September.

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