IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v343y2019icp67-89.html
   My bibliography  Save this article

A two-phase-like proximal point algorithm in domains of positivity

Author

Listed:
  • Gregório, R.M.
  • Oliveira, P.R.
  • Alves, C.D.S.

Abstract

This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted Lp (p=1,2) centers of mass are performed to demonstrate the practical feasibility of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:67-89
    DOI: 10.1016/j.amc.2018.09.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308336
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.09.054?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. O. P. Ferreira & P. R. Oliveira, 1998. "Subgradient Algorithm on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 93-104, April.
    3. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. da Silva Alves, Charlan Dellon & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros, 2021. "Lα Riemannian weighted centers of mass applied to compose an image filter to diffusion tensor imaging," Applied Mathematics and Computation, Elsevier, vol. 390(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. Broda, S. & Paolella, M.S., 2009. "Evaluating the density of ratios of noncentral quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1264-1270, February.
    5. Wiens, Douglas P., 2021. "Robust designs for dose–response studies: Model and labelling robustness," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    6. João Carlos de O. Souza, 2018. "Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 745-760, December.
    7. 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.
    8. 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.
    9. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    11. Eduardo Abi Jaber & Bruno Bouchard & Camille Illand & Eduardo Jaber, 2018. "Stochastic invariance of closed sets with non-Lipschitz coefficients," Working Papers hal-01349639, HAL.
    12. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    13. X. M. Wang & C. Li & J. C. Yao, 2015. "Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 202-217, January.
    14. Baringhaus, Ludwig & Gaigall, Daniel, 2017. "Hotelling’s T2 tests in paired and independent survey samples: An efficiency comparison," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 177-198.
    15. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," SciencePo Working papers Main hal-00972868, HAL.
    16. Yassine Sbai Sassi, 2023. "The Ordinary Least Eigenvalues Estimator," Papers 2304.12554, arXiv.org.
    17. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    18. Guo-ji Tang & Nan-jing Huang, 2012. "Korpelevich’s method for variational inequality problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 54(3), pages 493-509, November.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:67-89. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.